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.
One possible plot could be Percy being bestowed with the powers of the God of Destruction accidentally. He then has to struggle with controlling these new, chaotic powers while still trying to protect his friends and the world. Maybe he accidentally causes destruction in places he loves, like Camp Half - Blood, and has to find a way to reverse it.
A possible plot would be that Naruto arrives during a time of unrest in the Percy Jackson world. His presence as the God of Destruction shakes up the balance of power. Some might see him as a savior, thinking his power can end the chaos, while others fear he will only make it worse. He would have to deal with the politics among the gods, like Zeus being suspicious of his power. Naruto could also encounter demigods who are both in awe and afraid of him. He might try to teach them some of his ninja ways, but this could lead to misunderstandings and more 'destruction' as they try to adapt his skills to their world.
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.
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.
Well, you could start by establishing the connection between their worlds. For example, the Gods could be the ones to bridge the gap between Naruto's ninja universe and Percy's demigod realm. Then, introduce a common threat that forces Naruto and Percy to work together. Naruto could use his Rasengan while Percy uses his sword to fight enemies. And the Gods could be either helping or hindering them depending on their own motives.
Well, one way could be through some sort of magical cross - over event. Maybe the gods in the Percy Jackson universe notice Naruto's great power and determination from his own world. They decide to bestow god - like powers on him, perhaps seeing him as a worthy addition to their pantheon. Another possibility is that Naruto somehow stumbles into a magical portal that connects his world to the Percy Jackson world and there, he undertakes a great quest that earns him god - hood.
If Percy became the God of Destruction in the fanfiction, his relationships would become very complex. With his enemies, they would be even more terrified of him. However, some of his former enemies might also try to ally with him, seeing his power as a means to their own ends. His relationship with his mother would also change. She would be worried about her son, but also proud of his new - found status in a way. Percy would have to navigate these new relationship dynamics carefully.
His relationship with Annabeth would become more complex. Annabeth might be worried about Percy's new power getting out of control. She would try to help him find a balance, which could lead to some arguments but also deeper understanding.
The plot might involve the Titan of Destruction targeting Camp Half - Blood. Percy and his friends have to come up with a plan to defend it. They could search for ancient artifacts that have the power to weaken the Titan. Along the way, Percy has to overcome his own self - doubts and fears.