The plot could revolve around Percy's relationship with his divine parents. Since Zeus and Hera have a complex relationship themselves, Percy might struggle with their expectations. Maybe he's caught in the middle of a power struggle between Zeus and Hera's different ideas of how he should use his powers. He could also be trying to unite the camps of different god - related demigods under his leadership as the son of two major gods.
One possible plot could be Percy discovering his new parentage of being the son of Zeus and Hera. He might struggle with the new identity as it goes against what he previously knew. For example, he could face challenges from the other demigods who are suspicious or jealous of his new status. He then has to prove himself worthy of this new heritage while also dealing with the complex politics among the gods.
The Titans could be the main antagonists. Even though they were defeated before, they might see Percy as a threat because of his powerful parentage. They could try to stop him from fulfilling a prophecy or gaining more power. For example, Kronos might have some remaining influence and try to manipulate events to destroy Percy.
Some of the minor gods who feel overshadowed by Zeus and Hera might be antagonists. In this fanfiction, they could see Percy as a symbol of the over - dominance of Zeus and Hera. They might plot against Percy to send a message to his parents. These minor gods could use their unique powers and their knowledge of the magical world to create all sorts of problems for Percy, from cursing him to setting up traps in his path.
I'm not sure about a specific 'Percy son of Zeus and Hera fanfic' that stands out above all others. However, you can try looking on fanfic platforms like Archive of Our Own. There, you can search for this specific type of fanfic and read the reviews to find a really good one. Usually, the ones with high ratings and a lot of bookmarks are worth checking out.
Power and responsibility are often themes. Percy being the son of two major gods has a great deal of power, and he has to learn how to use it responsibly. Also, acceptance is a theme. He has to gain the acceptance of the other gods and demigods who may be skeptical or even hostile towards him at first.
One possible plot could be Percy's struggle with his new identity as the adopted son of Zeus. He might face envy from other demigods who don't understand why he was chosen. He could also have to deal with Zeus' overbearing nature as he tries to train Percy in godly powers. And there would likely be new quests that involve both his ties to Poseidon and his new relation to Zeus.
For the plot of this fanfic, it could start with Naruto having strange dreams about a powerful couple. These dreams lead him on a quest to discover his true identity. Once he realizes he is the son of Zeus and Hera, his life changes completely. He is now part of two worlds. In the shinobi world, his old enemies become even more wary of him, and some new allies emerge because of his new status. In the divine world, he has to learn the ways of the gods and deal with their complex relationships. There could be a main antagonist who wants to destroy the balance between the two worlds, and Naruto is the only one who can stop it. He uses his ninja skills combined with his divine powers to face this threat.
Well, perhaps the plot involves Percy being hunted by various forces. The Olympians see him as a threat because of his Chaos lineage, and the minions of Chaos might think he's too much of an Olympian. He then has to form an unlikely alliance with some demigods and minor gods who believe in his unique potential. Along the way, he uncovers secrets about the origin of the gods and the true nature of the relationship between Hera and Chaos.
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.
One idea could be Percy discovering his connection to Hera later in his adventures and having to deal with the reactions of his friends. Another could be him having unique powers inherited from Hera that set him apart from other demigods.