In this story, Izuku is the son of Aizawa and Inko, with Inko being the sister of Momo's mother; who's quirk is Creation. Aizawa's quirk and Creation fused to make a quirk that works just like Momo's, but with a few differences.
See, Izuku inherited a stockpiling factor from someone in Aizawa's Quirk Ancestry. Izuku creates his objects using the Anti-Energy (This is what Izuku calls it) his quirk stockpiles. This means that anything Izuku creates has a quirk suppressing nature. (This means that should Izuku create let's say Titanium, it would be legitamate Titanium but it would also retain the ability to cancel out the powers of whoever touches it. Izuku is an exception to the cancelation however.)
However just like Momo, Izuku can make anything non living, just using his inner stockpile instead of his fat. This means that any thing Izuku creates will always have a property that cancels out other people's quirks, however for mutants it makes them extremely tired lethargic. So much so that they cannot move. (If you watch One Piece, it works like Seastone on a Devil Fruit user)
This has a fun little side effect of making anything that interacts with the quirk factor inside Izuku's body fill his stockpiled energy extremely fast. (So if DNA left his body and was analyzed it wouldn't do anything) When depleted, he can eat someone's DNA, and when it gets to his esophagus it goes through a little filter that strips the DNA of its quirk factor and turns it into Anti-Energy. The amount injested equates to the amount of Anti-Energy has gets.
(By the way just an idea but mabye you could say that All for One works by slowly encasing the other person's quirk factor with Anti-Energy, copying it when it's completely encased, and then flooding the encased quirk factor with the same energy, deleting the quirk factor from their bodies. Since the 'stolen' quirk is surrounded by Anti-Energy, it stunts the quirk's growth inside of AFO himself, meaning it can no longer grow or have the chance to awaken until it's given away, where Anti-Energy isn't as present.)
(This would explain why AFO doesn't train his stolen quirks, merely stacks them along each other as well.)
You could make this be a huge deal to the police and prisons as well. Since Canon never confirmed the existence quirk suppressing cuffs and things like that you could make it so Izuku created them, as well as having Izuku supply an Anti-Quirk Barrier for UA after theirs is Decayed by Shigariki. (Fun fact, if All Might used OFA on a barrier made by Izuku he'd break his hand because by touching the barrier, his quirk gets canceled but the momentum does not.)
Downsides:
It's is a Stockpile Quirk, which means that if you run out of the stockpiled energy, you can't use it anymore.
Absolutely EVERYTHING Izuku makes has Anti-Quirk properties. It is not an option he can turn off. (Even the liquids and gases!) This makes him abysmal in Quirk Support.
If completely emptied, the stockpile takes an entire day to passively refill unless someone interacts with his quirk factor or he eats someone else's. (So Aizawa suppressing it, AFO trying to steal it[if you take the suggestion] or eating someone's DNA)
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MHA Story And Quirk Ideas
FantasyStory/Plot and Quirk Ideas I have no motivation to make, but think sound really cool! The entries with Quirk : [Name Here] means this entry is about a quirk idea! The entries with Story: [Name Here] means it's a story idea! If they're combined, it m...