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.
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.
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.
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.
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, 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.
The plot could revolve around Naruto being the son of a Greek god and how that affects the balance between the ninja world and the world of Greek mythology. His existence could be a threat to some dark forces in both worlds. These forces might try to eliminate him before he fully realizes his potential. Naruto, being the hero he is, would fight back and in the process, try to bridge the gap between the two different mythologies, bringing new forms of cooperation and understanding.
Another plot idea is that Naruto's powers as the'son of god' are slowly awakening. As they do, he starts to have visions of the past and future of the ninja world. This makes him determined to change the course of history to prevent future disasters, but he has to convince others to believe in his visions first.
He might have the power of instant teleportation. Just like a god can appear anywhere, Naruto could do the same to surprise his enemies or reach his friends in need quickly.