The kid could be a descendant of an old enemy of Konoha. But Naruto believes in second chances and redemption. So when he meets this kid who is in a difficult situation, he adopts him. The kid might initially be distrustful of Naruto and the people of Konoha, but over time, with Naruto's guidance, he starts to fit in and becomes a valuable part of the village.
Perhaps the kid is from a foreign land that Naruto visited during one of his missions. The kid could be an outcast in his own place because of some unique trait. Naruto, being the kind - hearted person he is, decides to adopt him. It could be that the kid has a different kind of chakra or a strange mark on his body that makes others afraid of him, but Naruto doesn't care.
The kid could be a young demigod whose parents are unknown. Maybe he's been living on the streets, hiding from monsters, until Percy finds him.
The kid could be a lost descendant of one of the old wizarding families. Maybe a long - lost relative of the Weasleys or the Blacks. Harry discovers this connection and decides to adopt the kid to preserve the family's legacy.
In this fanfiction, maybe the kid has some special power that Naruto notices. So Naruto adopts the kid to protect him from those who might misuse his power. Along the way, Naruto helps the kid come to terms with his power and they form a really strong bond, facing all kinds of challenges from other villages and ninja clans.
Maybe Percy discovers a kid in a difficult situation, like being an orphan in a monster - infested area. He decides to take the kid under his wing to protect him from harm.
It's possible that the kid is a result of some sort of time - travel or alternate reality situation. Maybe the kid is actually Naruto from a different timeline or dimension, and Naruto has to figure out how to deal with this strange situation while on his training trip.
Well, it could be that the kid has some special powers just like Harry. Harry sees himself in the kid and decides to take him under his wing. Maybe the kid is an orphan too, and Harry wants to give him a better life at Hogwarts, away from the cruel muggle world that didn't understand him when he was a kid.
It could be a bully in the village. This bully could constantly pick on Naruto because of his status as the Jinchuriki of the Nine - Tails. He might try to steal Naruto's food or prevent him from playing with other kids.
Well, one possibility could be a crossover where Naruto somehow ends up in the world of Death the Kid. Maybe Naruto's chakra is mistaken for some kind of unique soul energy. And Death the Kid, being the perfectionist he is, might be intrigued by Naruto's unruly and yet powerful nature. They could team up to fight some common enemy that threatens both their worlds.
A plot could revolve around Naruto trying to enter the Ninja Academy. He has to face all kinds of challenges, not just the physical tests but also the prejudice of the teachers. However, through his determination and some unexpected help from a kind - hearted shinobi, he manages to prove himself worthy of being a student at the academy.
The plot could be that a kid from a small village is kidnapped by a group of ninjas from a rival village. Naruto hears about it and sets out on a journey to save the kid. Along the way, he overcomes various obstacles and battles the kidnappers to rescue the kid and return him safely home.