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.
A potential plot could be Percy being sent on a special mission by Zeus. This mission might be crucial for the balance of the godly world, and Percy has to prove himself worthy of being Zeus' adopted son. He could face many obstacles and powerful foes during this mission.
One possible plot twist could be Percy's struggle with his new identity. Since Zeus is the king of the gods, Percy might face a lot of envy and even threats from other demigods or minor gods who see him as having an unfair advantage. Another twist could be Percy's relationship with his old friends at Camp Half - Blood. They might feel betrayed or confused as to why Percy has been adopted by Zeus instead of Poseidon.
His personality could change in several ways. For one, he might become more arrogant due to the association with Zeus. However, he could also become more responsible, realizing that he now represents Zeus in a way. He may also grow more distant from his old friends as he has to adapt to his new life among Zeus' domain, which could be full of more formalities and power plays.
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.
Hera could be a main antagonist. Since she's often jealous and protective of Zeus, she might not be happy with Percy being adopted. She could try to undermine him at every turn. Another could be Ares. He might see Percy as a threat, especially if Percy starts to gain more power as Zeus' adopted son.
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.
It could also be about power. Percy might realize that with Zeus out of the way, he can reshape the world of the gods in a more just and fair way. He could believe that Zeus's rule is corrupt and that killing him is the only way to bring about real change.
Yes, there might be. Fanfiction is a vast world, and with the popularity of Percy and the Greek mythology concept, it's quite possible that someone has written a story where Percy is Zeus' mate. You can check popular fanfiction websites like Archive of Our Own or FanFiction.net.
In this kind of fanfiction, Percy might challenge Zeus over issues like the unfair treatment of demigods. For example, Zeus could be overly harsh on demigods who make minor mistakes while the gods themselves get away with much worse. Percy, being a hero, would stand up for his fellow demigods.