In this fanfiction, Percy might encounter different versions of his friends. For example, Annabeth could be a powerful sorceress instead of a strategist. He could also face new and strange monsters that are unique to that universe.
Well, perhaps Percy could find himself in a dimension where the laws of physics are completely different. He might have to learn new ways to use his powers. For example, if water behaves strangely there, like it's solid in some areas and gas in others, he'd have to adapt quickly.
In fanfiction, if Percy Jackson goes to the Naruto universe, he'd probably be really confused at first. The chakra system would be so different from his demigod powers. But he could learn about it. And his ability to control water could be seen as a really unique jutsu. He might even be mistaken for a very powerful water - style ninja at first. He could also introduce the idea of Greek gods to the Naruto characters, which would be a really wild concept for them.
He might encounter new and strange creatures. In many fanfictions, Percy could meet unique magical beings that don't exist in his own world. For example, he could come across sentient plants that can communicate or floating islands with their own mini - ecosystems.
Maybe it's a corrupted version of one of the gods from Percy's world who has gained even more power in this new dimension. They could be trying to spread chaos and destruction, and Percy has to stop them. This antagonist would know Percy's weaknesses from their time in the original world, which would make the conflict more intense.
He could meet other demigods from different pantheons. Since it's a different world, there might be demigods associated with gods that Percy has never heard of before.
Another possibility is a new character that is unique to the other universe. This character could be jealous of Harry's arrival and the power he might bring from his own universe. So, this character tries to stop Harry from exploring and potentially changing the new universe.
Percy going to Ilvermorny would be a wild ride. First, he'd be amazed by the castle itself. The four houses would be a new concept for him. He might be sorted into a house based on his heroic nature, like Thunderbird perhaps. He'd introduce the idea of Greek gods to the students there, which would cause quite a stir. And his relationship with Annabeth would be put to the test as they are separated by different magical institutions.
Well, perhaps in the other universe, Harry finds that Voldemort is actually a hero. This would completely flip his understanding of good and evil. He could also meet alternate versions of his friends. For example, Ron could be a super - intelligent wizard instead of the more laid - back character he is in the original universe. And Hermione might be a powerful athlete rather than a bookworm. This would create a lot of interesting interactions and character development for Harry.