Melf's acid arrow fits the bill.
Damage on a miss has a very vocal minority opposition, especially here.
"Here," where? In the rules?

Seriously though: I don't know if I'm truly in a "minority" but I am certainly vocal about it: I hate damage on a miss. It would be the first thing I houseruled out, if it somehow made its way into the PHB.
But that's not really helpful, and my opinion (minority or not) isn't really the point of the discussion.
If I were looking to add more DoaM to my game, from a martial source (which is the most contentious way of getting DoaM I think), I'd try to find a way to do it using the existing rules in the game. I'd find some kind of analog in the game to us as an example, and then switch it around.
The first thing that comes to mind is some kind of a spell, and the lowest-level spell that I could find that meets our criteria (an attack roll with damage on a miss) is
Melf's acid arrow. This is a 2nd level evocation spell, and is only available to Wizards. When you cast this spell, you make an attack roll against a target; if you hit it takes X dice of damage and then takes X/2 dice of damage on its next turn. If you miss, it takes only X/2 dice of damage and none on its next turn.
Now. With all that in mind, let's make it a martial attack.
Melf's acid arrow is a 2nd level spell, which means it shouldn't be available as a feature until 3rd level. It's restricted to only one class, too, so this should be as well. (I nominate the fighter for obvious reasons.) And just as a wizard can't cast MAA at will, this ability too should be a limited resource. Considering all these balances, it might be easiest to make this a combat maneuver, available to the Battlemaster (and maybe those dedicated individuals who take the proper feat).
Something like this, perhaps?
Decisive Attack
When you make a melee weapon attack on your turn, you can expend one superiority die to deal an extra X damage to the target. If you miss, the target still takes this extra die of damage.
Anyway, that's just my two coppers. Like I said before, I'm not a fan of damage-on-a-miss and I wouldn't allow it at my table...but if I did, maybe this would be a good place to start?