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.
Some stories could involve the OC son of Zeus going on heroic quests. He might have to face powerful monsters or overcome difficult challenges that test his strength and wisdom, which he has inherited from Zeus in some way. Maybe he has to retrieve a powerful artifact to prove his place in the pantheon.
Another theme is the clash of cultures. The OC often represents modern values or different cultural backgrounds, and when they meet Zeus from ancient Greek mythology, there are clashes and reconciliations. This can lead to stories about acceptance, change, and the evolution of both the characters and the world they inhabit.
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.
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.
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.
There is definitely some out there. One aspect that might be interesting in these fanfictions is how Percy's powers could be different since his parentage is from Zeus and Hera. In many traditional stories, Percy is a son of Poseidon, but in these fanfictions, he could have lightning - based powers or other abilities related to Zeus and Hera's domains.
One idea could be Percy having to mediate between Zeus and Hades during a major feud. Since he's the son of both in this fanfiction, he has a unique connection to them. He could use his powers and his knowledge of both of their domains to try and broker peace.
One possible aspect in this fanfiction could be Percy's struggle with his new identity. As the adopted son of Zeus, he might face challenges in a world where the relationships between gods and their offspring are complex. He could be dealing with the expectations of Zeus, which are likely to be high and different from what he has known before.