Amelia_Dreemurr
Kyoto, Japan, with it's small crimes and even smaller family-owned stores. Izuku Midoriya has lived here his entire life and knows everyone, but holds dreams to leave for Musutafu, where the most expensive private high school resides. Lower-middle class with a single mom, he's stuck in a crappy Aldera Junior High with his old childhood friend and current school bully, Katsuki Bakugo, who has the same dream and can actually afford it. Scorn and mocking meets him at every turn, but he refuses to let it get him down. He'd been working hard his entire life, and all his savings would not go to waste.
Meanwhile, Toshinori Yagi, head of police in Musutafu, visits an old friend in Kyoto and helps the town's sheriff solve a murder mystery. In the midst of the chaos, he meets the young Izuku, saving him from a crazy blonde girl with a knife, the supposed culprit of the murder. Doing so, he loses her and loses his opportunity to catch such a dangerous individual, which leaves the insecure Izuku feeling guilty. He promises to make it up to him, but Toshinori takes pity for the meek, bruised, and banged up kid.
Upon their first encounter, Izuku confides about his dreams and Toshinori knows he could do something to help him achieve it. He doesn't even need to prove he's worthy of help, seeing how much hard work went into all the money he's earned over the years is enough to convince the policeman he's fully capable of succeeding.
With Inko Midoriya's permission, Izuku is put into his custody, and he moves to Musutafu with him. As someone who went to Yuuei Academy his former years, he's was allowed to grandfather someone in, but never had a kid to do so until now.
There are a few minor problems, of course, like Katsuki having been accepted in easily and now taking the same courses as him, but the major ones arise quickly. The blonde girl didn't live in Kyoto, and she wasn't alone... Musutafu suffers when criminals begin to form groups.