Taser

1 - Does one already exist in D&D?

2 - If it does not, how would you make one? Melee/stick version and Ranged/dart version

It depends on what you mean by "taser".

If what you're looking for is a non-lethal way to subdue someone, the rules already allow any melee attack to do that.

If what you're looking for is something that deals electrical damage, there are already spells that do that (like Shocking Grasp) and various ways of making weapons deal lightning damage (like Elemental Weapon).

The Armorer Artificer's Infiltrator armor also has a lightning-based ranged attack that might fit the bill.

A club or wand that does the shocking grasp cantrip but it is always non lethal is the closest i can think to make one as an object. 

Maybe a dart that does shocking damage and forces a con save or target has the paralysed condition for one round.

There's a bunch of thematically-appropriate stuff, as wargnarokkr's pointed out, but I'm not sure there's an official 'taser' like device. Guaranteed to be something in the homebrew section, though.

If I was making it, I'd go for something like...

Cartridge Taser
Type: Simple Ranged Weapon
Damage: 1d6 Lightning
Properties: Ammunition, (Range 10/20), Light, Loading
Mastery: Topple

Stun Gun
Type: Simple Weapon
Damage: 1d8 Lightning
Properties: Light
Mastery: Topple

I might switch out Topple for something like Sap and give them a standalone effect like, "must succeed on a DC 13 Constitution saving throw or fall prone." That would let me add charges, which is probably better for balance.

Quote from GnollitAll78450 >>

A club or wand that does the shocking grasp cantrip but it is always non lethal is the closest i can think to make one as an object. 

Maybe a dart that does shocking damage and forces a con save or target has the paralysed condition for one round.

 
Since at least the 80s, a lot of D&D tech weapons have a potential to malfunction on certain rolls.  Both to play homage to this longstanding tradition and more accurately reflect reality, I would say that the non-lethal rider is negated on a critical hit and critical damage reducing the target to zero would prove fatal.

A taser is basically a weapon that does a small amount of lightning damage with a stun rider (probably with a save -- it's by no means 100% reliable even against what are basically commoners, let alone high level PCs and monsters).

Quote from Caerwyn_Glyndwr >>

Quote from GnollitAll78450 >>

A club or wand that does the shocking grasp cantrip but it is always non lethal is the closest i can think to make one as an object. 

Maybe a dart that does shocking damage and forces a con save or target has the paralysed condition for one round.

 
Since at least the 80s, a lot of D&D tech weapons have a potential to malfunction on certain rolls.  Both to play homage to this longstanding tradition and more accurately reflect reality, I would say that the non-lethal rider is negated on a critical hit and critical damage reducing the target to zero would prove fatal.

This was a "Vague idea to point you in the right direction" and they could fill in the blanks with their own world details. I have no idea if they wanted an Aether-punk version, a technological version, or what. 
If I wanted to be accurate to the real-life version I would also have also come up with a "Cardiac complications chart" with chances of 'A-fib' 'V-fib' and 'total cardiac arrest' calculated out.

Also, yeah, i am well aware of malfunction chances, I am also well aware of how often they are ignored or discarded, so why bother? The core fantasy of a Taser is reliable non-lethality.

You could easily have a weapon that does lightning damage instead of its normal damage and say it's always non-lethal. However if it's something like a club, you'll have to whack most creatures many many times before they go down. This doesn't properly simulate the (reputation) effects of a taser/stun stick.