I have a player that is a dragonborn paladin. I have a story arc planned that may involve the possibility of ascending to a higher state of being and embracing his draconic ancestry. Is there a character builder or race builder stats for creating a half-dragon dragonborn? The Half-dragon builder in the monster manual is better suited for making monsters.

That is the only official half-dragon template. But it’s not nothing. The blindsight and dark vision and the buff the breath weapon is no joke. If you add wings with an hour of flight after 11th-level then that’s pretty baller.

A Dragonborn turned into a half-dragon would gain 10ft of blindsight, 60ft of Darkvision and a breath attack equivalent to the breath attack a wyrmling of their dragon half gets.

The breath weapon is the biggest issue as depending on what type of half-dragon they are, the damage they deal with it suddenly triples and it becomes a recharge ability. As it's a player ability, you should make it a once or twice / short rest instead of recharging on a 5 or 6. If you feel like the damage they deal with their breath weapon won't affect the balance of the game too much, you can keep the damage as is, otherwise I'd just increase the number of hit dice used in their breath attack by a number you feel comfortable with.

I don’t think recharge 5-6 is that big of an issue by itself, but you could easily change it to PB/long rest or something.

The problem with a recharge ability like that is that the player will use it in nearly every encounter, and always straight away to hopefully get another shot with it. I'd give the players up to 3 charges, with a cooldown and a recharge of one use per long rest, so they can save it up for a rainy day, as it were.

So what if they use it every fight?

Quote from IamSposta >>

So what if they use it every fight?

It would become a bit unbalanced, in my opinion. Getting effectively one free powerful spell every 6 rounds is quite a boost, particularly if it comes with other bonuses like wings, blindsight and darkvision and no negatives. Not a problem if they are on their own, but it could cause a character to outshine everyone else, which detracts from everyone else's experience.

Plus, in my opinion, abilities which players have to ration themselves with are much more interesting than ones which they can basically use every chance they get with impunity. It would be the equivalent of letting a barbarian have infinite rages, or a wizard infinite spell slots - these things are balancing mechanics put in place to make people think "should I or shouldn't I?". As said, if they have access to a breath weapon for every encounter, they will use it for every encounter, and it goes from being something special as it is now to just their default opening move, which to my mind is so much of an upgrade as to make it less fun. Giving them 3 uses per long rest with a 6 turn cooldown still makes them think about whether it's worth using, whilst it still clearly being an upgrade.

A Barbarian does get infinite rages at 20th-level. And a Wizard does get practically unlimited spell slots starting at 18th-level.

Quote from IamSposta >>

A Barbarian does get infinite rages at 20th-level. And a Wizard does get practically unlimited spell slots starting at 18th-level.

Ok, but both of these are reliant on the level of the character (we don't have that) and dedication to their chosen class, in the case of the barbarian, absolute dedication.

What we're talking about here is a racial trait, and as such is independent of player level. This isn't something rewarded for leveling up, it's something else. For example, if this player is a level 20 barbarian, now they will have unlimited rages and  infinite ranged magical attacks. Meanwhile, the level 20 dwarf barbarian just has the rages, and feels somewhat outclassed.

to pre-empt a potential rebuttal, whilst you could give the dwarf barbarian a magical item or two to keep them in line, there's nothing to stop the half-dragon barbarian from also having magical items. 

What we're discussing giving the character is 100% bonus, possibly earnt through roleplay but it is an option which is closed to all the other players who aren't dragonborn, and that makes it a potential cause of imbalance which is remedied by giving them limited use of it. 3 uses per long rest is still 3x as good as their natural breath weapon, and the attack is better.

Normal breath weapon is 1ce/short rest..

And the normal breath weapon becomes practically useless at higher levels.

Quote from IamSposta >>

Normal breath weapon is 1ce/short rest..

And the normal breath weapon becomes practically useless at higher levels.

My apologies, I thought it was once per long rest.

I would still consider it best if it were tempered to 3 times per short rest, with a cooldown. Or 3 times, recovering one per short rest, with a cooldown, to prevent them just having a short rest every 3 encounters to keep the powerful breath weapon going for every combat.