So I have a player who wants a bow that he doesn't have to worry about tracking ammo for. I have come up with a couple of ideas, so a magical quiver with 20 arrows that, every long rest, gets replenished, or a bow that always has an arrow in place when drawn. But I wondered are there any magic items already out there that I could use that do a similair thing (or could help me get a price estimate)? 

The dragon wing bow from Fizban's produces its own ammo

The Artificer gets an infusion (returning crossbow I think, or something like that), that if you don't have Ammu itoon in it, it creates its own - in other words, it has unlimited ammo.

You could also just take a easy route and say he does not need to track arrows.  Just assume that he recovers arrows after fights and loots any arrows he finds in the quivers of corpses to make up for any of his arrows that are damaged or could not otherwise be reused. 

Is it technically the right way to play?  No, but melee characters and casters (with an implement to cover free material components) do not need to keep track of their ammunition, so it really is just adding some busywork to range characters for the sake of adding busywork.

Though a magic item would also work, this allows you to make more interesting magical quivers or the like moving forward, providing a more enjoyable boon than “congratulations, now you do not need to do something that the rest of your party already did not have to do.”

You could make a bow that tracks its own arrows as long as they are in the firing range of the bow.

This would give the player a better chance at collecting the fired ones. It would also give him a chance to track something with an arrow still in them. At least until it breaks or falls out. Nothing is stopping the victim from firing the arrow away from themselves if they ever think thats how they are being tracked.

Or let the quiver refill at a rate of 5 normal arrows a day until full. It would limit the power of the quiver.

My table tracks ammo and component use. It doesn't take any extra time. Think of all the time just listening to the other players during their rounds. There is nothing saying you can not carry extra ammo.

Quote from Linklite >>

The Artificer gets an infusion (returning crossbow I think, or something like that), that if you don't have Ammu itoon in it, it creates its own - in other words, it has unlimited ammo.

 It's called Repeating Shot.

Honestly, I don't even bother requiring players to track nonmagical ammunition for ranged weapons under normal circumstances.  I figure that they can recover and/or craft their own in their downtime enough to insure that they've got enough unless something actually happens to separate them from their supplies.  Arrows and other ammunition in D&D are cheap enough that you can buy all you'd ever need for pocket change anyway.

Quote from Caerwyn_Glyndwr >>

You could also just take a easy route and say he does not need to track arrows.  Just assume that he recovers arrows after fights and loots any arrows he finds in the quivers of corpses to make up for any of his arrows that are damaged or could not otherwise be reused. 

Is it technically the right way to play?  No, but melee characters and casters (with an implement to cover free material components) do not need to keep track of their ammunition, so it really is just adding some busywork to range characters for the sake of adding busywork.

Though a magic item would also work, this allows you to make more interesting magical quivers or the like moving forward, providing a more enjoyable boon than “congratulations, now you do not need to do something that the rest of your party already did not have to do.”

Or just have a monthly stipend the adventurers spend for things like inn lodging, food, and baths.  Since he has ranged ammo, you add a bit to theirs unless they make it a point using downtime activities to fashion arrows.

I typically track ammunition until level 5, and then I don't UNLESS it's some sort of mega expedition but when that happens I inform them hey, you're gonna be out of town for a long time with no chance to resupply, stock up.

Quote from 6thLyranGuard >>

Quote from Linklite >>

The Artificer gets an infusion (returning crossbow I think, or something like that), that if you don't have Ammu itoon in it, it creates its own - in other words, it has unlimited ammo.

 It's called Repeating Shot.

 You're right. In thinking of returning weapon, that allows you to throw your weapon and it returns to you. My Artificer has both.

I've never DM'ed or played in a game where we tracked ammo.  It seemed like there was enough going on already and keeping track of every detail would have slowed things down too much or made things frustrating for a bow using character.

I actually like your replenishing quiver the best though. 

It always boggles my mind how people discard ninety percent of the rules for exploration, i.e. things like travel time, random encounters, navigation, encumbrance and supply, and all the rest, and then complain that the game does a poor job with exploration.  If y'all want that stuff, then use the rules.  And rather than saying "Oh, high-level features negate the need" and skipping it altogether, let high-level features do their job.  It's almost like those features should be a reward that helps the players adventure more, huh?

Anyways.  The simplest magic item would simply be an archer's ring that lets the character find ammo they fire while wearing it.  Unless the arrow breaks, is carried off by a creature escaping, or sails into impassable terrain, he can get it back.  I wouldn't even make him decrement his ammo for a shot he can recover; let him know if an arrow goes somewhere he can't get back that he needs to decrease his available supply by one.

Beyond that, an efficient quiver is there very much to obviate ammo issues; could simply let him find one of those, tell him to cough up three gold every time he hits town to resupply, and then say "You have enough mundane ammo for any normal adventure" without bothering counting arrows.  Or, as was said, allow him to use the item as an excuse not to track individual mundane shots.  I don't necessarily agree with "tracking ammo is a stupid pointless waste of time and if you do it you're bad at D&D forever and should just stop playing", but a magic item specifically dedicated to Storing Archery Supplies should be allowed to make life easier for archers.

It kinda boggles my mind how much people complain about tracking ammunition on a digital sheet where it literally takes a click or two to adjust....

I get that it's not the immediately "immersive" part of a character. But when you are down to your last three arrows, and that dark thing is hunting you in the forest- it gets pretty damned immersive. 

By constantly wanting to cut out any kind of resource management, there is a risk of curtailing (some of) DM's ability to create exciting or immersive experiences. 

See, exactly!  Exactly!

Resource management is not ever going to be an Immersive Storytelling Tool by itself.  Nobody ever tells stories about that one time they counted their arrows on the wagon ride along a secure road between two well-defended cities...but as an additional pressure in tense situations?  That's when resource scarcity becomes a critical part of the game.  It's an important tool too many DMs dismiss out of hand because their players whine.  Well, hey - children whine when you give them medicine.  Doesn't stop any reasonable parent from doing it, ne?

As a DM, I most certainly don't want to track ammunition for monsters, and the whole point of component pouches and foci is to eliminate tracking of spell components (plus cantrip ammunition is unlimited), so I'm not sure why archers should have an extra tax.

The efficient quiver can hold 3 pounds worth of arrows, 36 pounds worth of javelins, and 24 pounds worth of staffs, so a magic item that is just "Any time you reach into this quiver it contains an arrow. Arrows removed from the quiver last until you pull a new one out" is hardly broken for an Uncommon item.

Cantrips not requiring ammunition expenditure is an oversight more than an argument, to me.  Cantrips are already superior to weapons in basically every way - they bypass mundane weapon resistance for free, a spellcaster cannot ever be disarmed of their cantrips, their cantrips take up no weight, space, or other encumbrance, and as it stands they require no expenditure to use outside of time.  The only thing holding cantrips back from completely obsoleting all weapon combat is that cantrips don't get ability modifiers or, generally, more than one strike.  Note that the only cantrip which breaks these rules - Eldritch Blast - is considered both the best cantrip in the game hands down, but also generally held to be the best form of reliable at-will damage in 5e when Agonizing Blast is taken into account.

I have heard some very convincing arguments for requiring mages to keep reagents on hand that are consumed with each casting of a damaging cantrip.  I have not implemented those rules in my own games mostly because I've also heard compelling arguments for allowing spellcasters to cast spells no matter their state, allowing them to access the basic fundamentals of their class whenever they need to.  But frankly, I could be swayed the other way.  Take away a ranger's bow and they can't access the basic fundamentals of their class.  Take away the barbarian's axe, he can't access his class fundamentals.  There shouldn't ever be such a thing as 'cantrip spell slots', but I'd be quite keen to see how the game shifted if every damaging cantrip automatically consumed a packet of elemental salts or some other form of reagent/'magic ammo'.

You do not have to track an NPCs or monsters stuff.

It's the characters responsibility to keep track of their own equipment. Seriously they do have the time at the table.

Quote from Yurei1453 >>

See, exactly!  Exactly!

Resource management is not ever going to be an Immersive Storytelling Tool by itself.  Nobody ever tells stories about that one time they counted their arrows on the wagon ride along a secure road between two well-defended cities...but as an additional pressure in tense situations?  That's when resource scarcity becomes a critical part of the game.  It's an important tool too many DMs dismiss out of hand because their players whine.  Well, hey - children whine when you give them medicine.  Doesn't stop any reasonable parent from doing it, ne?

 In the 90's I often played in convention games where things were tracked such as arrows and spell casting components and there even were times in the 80's when a player forgot to buy some type of consumable in town and lead to an issue to over come. I also played in a post apocalyptical game in which resource management was essentially the whole game and failure to have/find resources was a huge impediment in overcoming game obstacles.

Having said that in AD&D and other flavors of D&D most games I have seen do not track such resources as the GM and group do not want to have that game experience and or immersion. An important note that as a GM I try and remind players when they are at a point they can buy stuff or if they are out of stuff that they should consider it. Why? Well the players are not the PC's and the PC's are not the player. So I as the GM are their to provide a link to the player on what I think their PC might and or would do based on the PC's experience. 

Session Zero: In general session zero and or a GM's game notes are often where I have seen how much resource management is going to be present in a game.

I have also seen issues with not tracking some resources in games, ie I bought 10 days of iron rations at level 1 and I have not bought any food and I am level 10, 5 years later. What do you mean I need to buy things like food, water, new cloths, replace equipment and pay for food for my heard of trained raptor's and alpha t-rex? 

Good Luck  

Quote from Yurei1453 >>

There shouldn't ever be such a thing as 'cantrip spell slots', but I'd be quite keen to see how the game shifted if every damaging cantrip automatically consumed a packet of elemental salts or some other form of reagent/'magic ammo'.

 Eh, if I wanted to make logistics a significant part of a campaign I'd slap a cost on every spell, get rid of spell foci, give component pouches charges, and get rid of spells like goodberry that exist to make logistics irrelevant. It's pretty clear that 5e decided that logistics is Not Fun, I don't see a reason to be inconsistent about it.

Quote from Yurei1453 >>

See, exactly!  Exactly!

Resource management is not ever going to be an Immersive Storytelling Tool by itself.  Nobody ever tells stories about that one time they counted their arrows on the wagon ride along a secure road between two well-defended cities...but as an additional pressure in tense situations?  That's when resource scarcity becomes a critical part of the game.  It's an important tool too many DMs dismiss out of hand because their players whine.  Well, hey - children whine when you give them medicine.  Doesn't stop any reasonable parent from doing it, ne?

 Kids also whine when you bring them along on "vacations" that are actually business trips to a hotel that's only got basic cable, no pool, a restaurant that makes the school cafeteria look like fine dining, and no kid-friendly attractions within a 10 mile radius.

Silliness aside, resource tracking takes a lot of work to actually make interesting, and D&D has never had rules that actually made things like finding food actually fun.  One or two people make a roll, and if they succeed then the party doesn't need to mark off a day's worth of rations.  Unless someone has the Outlander background, in which case no roll is necessary unless you're traveling through a volcanic wasteland or a city (unless you're fine with living off roof rabbit).

Trust me, tracked food, water, and ammo gets real effing interesting real effing quick when you start to run out.