I'm not sure specifically as there could be many different takes on it. It might be about Naruto having a divine or semi - divine heritage as the son of a minor god, which could lead to all sorts of new adventures, powers, and interactions with the Naruto universe's existing elements.
Obviously Naruto would be one of the main characters since it's about him being the son of a minor god. There might also be the other regular characters from the Naruto series like Sasuke, Sakura, Kakashi etc. who would interact with Naruto in this new context.
Perhaps Percy discovers that he has some latent powers related to being the son of a minor god that he didn't know about before. This could lead to him having to train in a whole new way, with a mentor who is an expert on that particular minor god. He might face challenges from other demigods who are jealous of his new - found abilities.
A satyr who has a special connection to the minor god. He could be like Grover, but instead of being dedicated to Pan, he's dedicated to this minor god. He could help Percy understand the ways of the minor god and provide some comic relief as well.
Another possibility is that Naruto's 'god' parent is an actual deity from Japanese mythology. Since the Naruto world is inspired by Japanese culture, it would make sense for a kami (god) from their mythology to be Naruto's parent. For example, Amaterasu, the sun goddess. Her power could be passed down to Naruto, giving him abilities related to fire and light.
It could be about Naruto having god - like powers inherited from his 'divine' parentage. Maybe he uses these powers to quickly end the shinobi wars and bring about a new era of peace in the ninja world.
Apollo could be a likely candidate. Apollo is the god of music, prophecy, and healing. Naruto's strong sense of justice and his ability to inspire others could be seen as traits inherited from Apollo. Also, Naruto has a certain charm that could be related to Apollo's association with the arts. And if Naruto had some healing abilities from Apollo on top of his own ninja skills, it would make him even more of a valuable asset in battles.
The Akatsuki could still be the main antagonists. Even though Naruto is the'son of god', they might see his power as a threat to their own goals. For example, Pain might believe that Naruto's new - found status will disrupt the cycle of pain and suffering that he wants to maintain in the world.
Well, perhaps the plot could involve Percy having to prove himself worthy of becoming a minor god. He might have to complete a series of difficult quests that test his courage, loyalty, and wisdom, which are the traits highly valued in the world of the gods.
Well, one possible plot could be that Naruto, as the second son of god, has some sort of hidden powers. Maybe he starts to discover these powers gradually as he faces various challenges in the ninja world. For example, he could have the ability to control certain natural elements in a much more powerful way than normal ninja techniques.