So obviously this is a self insert book, but I have taken the liberty of giving you a backstory. This backstory is not meant to give your character a specific race(or gender if I can help it) so if I accidentally insert my own adjectives or pronouns please comment and call me out so I can fix it.
Here we go.
You are All for One's child. Your quirk is his, but more developed. You can take the power of anyone standing in the same room as you(your range increases the more you train), and you can even take away quirks so they can no longer activate them once you have made contact with that person. You can permanently take someone's quirk for yourself, but it kills them. You have only done this once.
As a child you once accidentally killed one of your father's associates after he held you for too long and you unintentionally drained him. He was dead in a minute. You were four. You later learned how to touch someone for an extended period of time without killing them, but you still hate physical touch because of this trauma.
His quirk was a musical quirk. Whenever he had a song playing through headphones or even stuck in his head, he could stop the movements of everything in his range. When the rest of the room could hear the song or he sang, he was able to control their movements like a puppet master. This quirk is now permanently yours.
After this incident, your father sent you abroad(to wherever you are actually from) to train with a companion of his there. This left him available to focus on his prodigy Shigaraki Tomura. You had never been his favorite anyway because despite you being more powerful than the boy, Shigaraki had ties with All Might, making him more valuable in the grand scheme of things. You were merely being designed to aid him.
Until you turn 17, you train abroad in a covert facility. You train day and night, increasing your range and capability. Your father's associate has you battle with many different quirks so you can practice using each of them. Soon you are able to not only drain someone's quirk, but also drain everything that they have cultivated and learned about it so that even with a quirk you've never used you can fight equally with your opponent. It doesn't take long for you to ultimately take someone's quirk and use it more powerfully than they can.
However, after you turn 17, All Might, who was working abroad at the time, found the facility and destroyed it. He found you and decided that rather than making an enemy of you he wanted to take you back to Japan. In the end you ended up staying with Aizawa(this is subject to change depending on the one-shot).
After readjusting to the culture, the heroes decide that it would be best for you to train as a hero at UA so as not to repress the power you didn't know how to live without.
Quick interlude: for the purpose of this book, which is not pedophilia, UA is a COLLEGE not a high school. not only does this give me more freedom as an author to sexualize the characters it also helps in the one shots with characters like Dabi and Hawks who are obviously adults. Therefore, the minimum age of the students is 18. Now back to the backstory.
At UA you make friends and all the fun things and blah blah blah. You do not tell the other students of your lineage or your quirk. As far as they know, you are an orphan Aizawa stumbled across randomly who happened to have a powerful musical quirk.
That should be everything.
Obviously the purpose of this book is for you to put yourself into this world, and my goal is to make y/n as dynamic as possible for the sake of the diverse audience reading this. This means that whenever I accidentally use adjectives or pronouns that are not all encompassing I would love for you as the reader to call me out so that this may be corrected.
Thank you, and please enjoy!