Hi, I was inspired to do this by the story 'How Eating a Strange Fruit Gave Me My Quirk' in where he eats a devil fruit and becomes awesome.
In this story, he will be pretty strong when he enters UA. he may get One for All, but you'll have to wait and see.
In the city of Musutafu, we find a young 8-year old Izuku Midoriya wandering the streets with his mother. Izuku was a rather short boy for his age, he was a scrawny and weak boy who just happened to belong to the 20% of the population that didn't happen to have a superpower, also known as a quirk. He was constantly bullied by his former friend. Currently, he and his mother Inko were on their way to the marketplace to buy groceries.
They passed an alleyway when he noticed something strange. Out of curiosity, he walked down the alley and found a nicely polished wooden box. He didn't know why but it felt like the box was calling for him. On top was a note that stated:
My name is Jozu. In this chest is a handful of my personal belongings from my traveling days. I used to be a traveler in a crew that explored the world. They were my family.
Anyway, one of the objects is a devil fruit that used to belong to one of my best friends before he passed away. I don't know if you know but devil fruits give you great power like coating your body in diamonds, which are called Paramecia which has a lot of random powers ranging from being made of rubber to being able to create earthquakes and tsunamis with a flick of the wrist. You are also able to or to become an element like fire or lightning, where objects like bullets just pass through you, these are called Logia. This one is what is called a zoan, which allows you to turn into a specific animal. This one allows you to turn into the Legendary Pheonix. Its flames allow you to heal other people. One weakness all devil fruits have in common is that they are weak to seawater and once you eat one, you'll never be able to swim, ever.
There are books on two ancient types of martial arts that I highly recommend you learn. One is Haki. It's not really a martial art, more of a technique that fits with every martial arts. It gives you either 2 or 3 abilities which all depends on your willpower. The first one is Observation Haki, it allows you to sense people that are hidden or if you master it enough, you can predict what an opponent will do before they do it. The second is Armament Haki. It allows you to create a sheet of armor around a certain body part. It can be used offensively and can counter devil fruit like the before mentioned Logia fruits. The third one, which is Conqueror's Haki, which cannot be trained as it only has a 1 in a million chance of appearing in someone. It allows you to force your will onto others making them go unconscious. It can also be used to tame animals.
The second martial art is called the Black Leg Style. As you might have guessed it focuses on you legs. We got this book from an allied crew called the Straw Hats. It was created for people who primarily use their hands to work, like cooks or blacksmiths. I never learned it but I hope you can master this style.
Also in this chest is a journal of sorts, full of our travels and adventures.
Hope you do well,
P.S The fruits taste like garbage.
Now Izuku was excited. He could gain a quirk! He opened the chest and looked into it. It didn't take long for him to find the fruit. It looked spectacular. It was blue with a mango-like shape. On it were black like spirals. Izuku bit into the fruit and immediately regretted it as it tasted even worse than Jozu said. He swallowed and ate the rest of the fruit. He found the books Jozu talked about and put them under his arm. As he walked out of the alleyway, he tried to activate his fruit and made the mental command to activate it. Immediately, green and black flames burst out. He started panicking until he realized that the flames weren't hurting him. He only had one thought going through his.
'So Cool! Maybe now I can become a hero!'
That's all Folks! The next chapter is a time skip to the entrance exam.
By the time he's at UA, he'll have mastered the basics of the Black Leg Style and starting the learn Diable Jambe. He'll have the Observation Haki part done and be halfway through Armament Haki. He will have Conqueror's Haki and unlocked when he was rescuing Bakugo from the sludge villain but can't fully control it.