The only reason Midoriya got to talking with Ashido was because his bandages needed reapplying. Still, this small hand of fate was all that was needed to spark a friendship and a far closer bond between the two classmates. I honestly have no idea what their ship name is, so I'ma call it MinaDeku

The First Generation of Quirked individuals had it rough. Yuuei is built as a school for the Quriked, but is in reality, just a way for the Quirkless to keep the Quirked in one place, contained. Faced with a world that despises and hates them, Midoriya Izuku and Ashido Mina and others join the very first generation of Heroes to change this worlds hatred of Quirks. MinaDeku,Kacchako

Midoriya had a latent quirk, causing One For All to activate strangely and release a different kind of power. Because of this his entry exam turns out a bit differently than expected.