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It's one of those hit with a quirk stories. In the first week of UA, before the USJ even happened, Todoroki's going to class but runs into a kid with an out of control quirk.
Said quirk makes him split into his left and right sides. So there's one Todoroki with completely white hair and only ice power, and another Todoroki with completely red hair and only fire power.
Weirdly enough, only the redhead has the scar.
Todoroki, both of them, goes to school anyways and explains to the teacher what happens. The kid turns out to have done this before and he's not sure how to reverse it, because he tried last time and it didn't work because quirks are complicated. There also didn't seem to be a time limit because the last guy spent almost a month separated.
But they did know how to undo it... sort of. The person who got separated has to reconcile his differing sides and then they'll be one person again.
Except Todoroki before his character development is incredibly stubborn and emotionally dead, so this is going to take a while.
Both Todorokis have to go to school until all of this gets fixed, and Kaminari comes up with the way of differentiating them. The kanji in his name, sho, means burning, and the other one, to, means freezing, so the redhead is now named Sho and the other To.
To make things more complicated, they also have different personalities.
Sho is angry, passionate, and holding all of the pent up rage about Endeavor and everything he hates. He's also incredibly stubborn about never using his fire, and rejects all of Endeavor's attempts to train him while he's separated from To. But Sho is also the part of Todoroki who still wanted to be a hero to save people.
To, meanwhile, is emotionally reserved and pretty chill, and most of the time it doesn't look like he cares about anything. He's very clinical and logical, only going to school and training to be a hero because he's told to. He's also the part of Todoroki who knows deep down that they can't save everyone without using both sides of their quirk, but To also knows that Sho isn't going to listen to him if he tries to convince him.
Everyone else, meanwhile, are getting incredibly concerned about the signs both Todorokis are showing, because Sho not using the fire he got from his dad but being fine with To using the ice he got from his mom who gave him his scar? Major red flags.
It's a really introspective fic where Todoroki's forced to confront the sides of himself and his issues sooner, and he ends up making friends in class 1A who help him get through his trauma and get him therapy.
Don't worry, they get Endeavor arrested soon enough.