One way it could work is if Naruto's immortality was a result of some powerful magic in the Percy Jackson universe. Maybe he was blessed by a god or came into contact with a magical artifact that made him immortal. His ninja skills would be quite unique in that world and could make for some interesting storylines, like teaching demigods his stealth techniques.
One way it could work is by having Naruto's powerful chakra be misinterpreted as the kind of godly power in the Percy Jackson universe. Maybe he arrives in that world accidentally through some sort of interdimensional rift. His ninja skills, like his shadow clone jutsu, could be seen as some strange and powerful magic there. And his determination and willpower, which are so central to his character in Naruto, could be what makes him seem like a 'god of destruction' in the context of Percy Jackson's world where the gods often have very strong wills and tempers.
In a Percy Jackson fanfiction where Naruto is the son of Susanoo, Naruto's ninja - like agility and stealth would be a great asset. Susanoo in Japanese mythology is a powerful entity, and if Naruto is his son in this fanfic, he could have some sort of control over powerful weapons or shields. He could use these in battles against the Titans or other enemies in the Percy Jackson world. Also, his ability to never give up, which is a big part of Naruto's character, would make him a formidable hero in this new setting.
Well, one way it could work is by having Naruto possess the speed and cunning associated with Hermes. Maybe he could use his ninja skills in the world of Percy Jackson. For example, his shadow clone jutsu could be a really unique ability there. He could send clones to gather information quickly, just like Hermes' messengers.
He could be a mentor figure. Given his immortality and vast combat experience from the Naruto world, he could teach the demigods new ways to fight and strategize.
One way it could work is that the spider powers could enhance his already existing skills. His reflexes, which are good from his demigod training, could be super - boosted by the spider - sense. And he could use his spider - like climbing ability to scale the walls of Mount Olympus or other mythical places that are otherwise hard to reach. This would give him an edge in battles against both mythical creatures and other demigods.
Well, in fanfiction, anything can be made to work. If Percy were Aphrodite's husband, it could lead to some really interesting power dynamics. Percy is a powerful demigod with his own set of skills and Aphrodite is the goddess of love. Maybe their union could bring a new kind of peace in the world of the gods and demigods. His skills in combat and her ability to manipulate emotions could combine in unexpected ways.
If Naruto was the son of Zeus in a Percy Jackson fanfiction, his character would have to adapt to a whole new world. The demigod world of Percy Jackson has its own rules and politics. Naruto, being used to the Hidden Leaf Village's system, would have to learn about cabins, quests, and the whole Greek mythology aspect. His shadow clones could be used in really creative ways during quests, like scouting ahead or fighting multiple monsters at once. And his ability to never give up would be a great asset when facing the many challenges that come with being a demigod.
In a crossover fanfiction, the settings could merge. For example, Camp Half - Blood could be visited by Naruto. The demigods would be intrigued by his chakra abilities, which are so different from their own powers based on the Greek gods. Naruto could teach them some of his ninja skills in return for learning about their combat techniques. And perhaps the Juubi's presence could disrupt the natural balance of the Percy Jackson world, leading to new and unexpected adventures for both Naruto and the demigods.
In a fanfiction where Percy Jackson is Thor's brother, it might involve some magic or divine intervention that made them related. Percy could introduce Thor to the Greek gods and their ways. This could lead to some cultural clashes and also opportunities for cooperation. For example, Percy could show Thor how the Greeks use strategy in battle, which is different from the Norse way of brute force. And Thor could teach Percy about his hammer and how to use it in combat. Their brotherly bond could be strengthened through shared experiences like fighting against a common enemy that threatened both the Greek and Norse worlds.
Another possibility is that the Sharingan is a magical artifact that has been lost in the Percy Jackson world. A group of demigods could stumble upon it during one of their quests. They might not understand what it is at first, but as they start to explore its powers, they realize its potential. However, they also face the danger of the Sharingan's negative effects, such as the overuse leading to blindness. This would add an interesting dynamic to the story as they try to balance using this powerful tool while avoiding its drawbacks.