Son of Zeus: Heracles was an American adventure film based on the comic book Hercules: The Battle of Thrace by the company of the Radical comics. The film told the story of Hercules, the great hero of ancient Greek mythology. Heracles was the son of Zeus, with great strength and a strong body. He had once completed the twelve trials arranged by Zeus and became a mercenary. Because of his past sins, he fought with five loyal companions. In the film, when King Thrace and his daughter sought help from Hercules, they faced the threat of barbarians. The film was directed by Brett Ratner and starred in The Rock Johnson and Ian McShane.
Clash of the Titans was a movie series about the battle between the son of Zeus and the other gods. The series included 2010's Clash of the Titans and the 2012's follow-up, Rage of the Titans. The story was about the adventures of Perseus, son of Zeus, and the other gods to save the world. The series was directed by different directors and had a strong cast, including Sam Worthington, Liam Neeson, and Ralph Fiennes. The movie showed the fierce battle and rescue operation between gods and humans.
Obviously, the OC son of Zeus is the central character. He's the one around whom the story revolves. But other common characters include Zeus himself. His presence, even if not always physical, looms large as the father of the OC.
A great antagonist could be a Titan who has a grudge against Zeus and sees Percy as an easy target to get back at him. For example, Atlas. He could try to use Percy to free himself from his burden again or trick Percy into doing something that would cause chaos among the gods. Another option is a powerful and vengeful demigod who feels that Percy, as the son of Zeus, has been given too much power and attention, so he wants to take Percy down.
It could be a powerful Titan who escaped from Tartarus and wants revenge on Zeus by targeting his son Percy. This Titan might have unique powers that make him a formidable foe.
One possible antagonist could be those in the ninja world who fear Naruto's new - found power. They might see him as a threat to the existing power structure. For example, some of the more traditional ninja clans could be against him.
In the fanfiction, Percy's relationship with Zeus may develop gradually. Zeus, being a powerful and often aloof figure, might initially be distant from Percy. But as Percy shows his courage and abilities, Zeus could start to take a closer interest. This might lead to Zeus mentoring Percy in some ways, teaching him about godly powers and responsibilities.
Power and its consequences are also a big theme. He has great power being the son of Zeus, but that power can attract envy and danger. So many fanfictions explore how he manages this power and the responsibilities that come with it. For example, in some stories, he has to use his power to protect the innocent without causing too much destruction. And it also makes him a target for those who want to use his power for their own gain.
In this fanfiction, Naruto's appearance might be different. Since he is the son of two powerful gods, he could have a more majestic look. His eyes might glow like lightning or have a special color. His story could involve him trying to fit in with the normal ninjas while also coming to terms with his divine parentage. He might face discrimination from some who fear his power, but he overcomes it with his kind heart, just like in the original Naruto story.
Yes, there are likely fanfics out there with this concept. The Harry Potter and Percy Jackson fandoms are both large, and some fans like to cross over the two universes in fanfiction. You can try searching on fanfic platforms like Archive of Our Own or FanFiction.net.