A cool plot could be Percy being sent on a quest that involves mending the rift between Zeus and Poseidon. Along the way, he meets old foes and new allies. He has to use his wits and the powers he got from his fathers to convince other gods and demigods to support his cause. For example, he might have to show the children of Zeus and Poseidon that they can work together instead of being rivals.
Perhaps Percy could be transported to a different realm where the rules of his dual parentage are completely different. In this realm, he's seen as some sort of anomaly. He has to figure out how to get back home while also dealing with the fact that his powers are acting up. He might meet a character who can help him understand his true potential as the son of Zeus and Poseidon.
Perhaps in the fanfiction, there could be a prophecy that involves Percy, Zeus and Poseidon. The prophecy states that only when the three of them perform a certain ritual together can they prevent a great disaster. But the ritual requires them to put aside their differences and trust each other completely. Percy has to convince the two powerful gods to participate.
A great plot could involve Percy discovering a hidden power within him due to his relation to Zeus. He then has to learn to control it while also dealing with the envy of other demigods. For example, he might accidentally cause some chaos in the camp which makes others suspicious and jealous of his new - found abilities.
One interesting plot idea could be Percy having to team up with a demigod child of Leto. They could go on a quest to find a long - lost artifact that has the power to restore balance between the sea and the moon's influence. Since Percy is the son of Poseidon, his control over water and the other demigod's connection to Leto's lunar powers would create a unique dynamic.
One interesting plot idea could be Percy having to deal with the conflicting natures of his 'parents'. Since Gaia represents the earth and Poseidon the sea, he might struggle with controlling both earth - related and sea - related powers. For example, when he's near a beach, he could accidentally cause small earthquakes or make strange things happen to the sea life. Another plot could involve Percy facing a threat that only his unique dual - heritage can defeat. Maybe an ancient evil that is both of the land and the sea, and Percy has to figure out how to combine his powers in a new way to stop it.
One idea could be Percy having to face a new and powerful sea monster that is awakened by an ancient curse. He'd have to use his powers in unique ways, maybe even discovering new abilities as the son of Poseidon. Another could be Percy traveling to a long - lost underwater civilization that has a connection to his heritage as an ancient son of Poseidon.
A great plot could be Percy getting into trouble in the mortal world and Poseidon having to come to his rescue without revealing his true identity to the mortals. This would create a lot of tension and interesting scenarios where Poseidon has to use his powers subtly. Also, they could be on a mission to save a group of sea creatures that are being hunted by an unknown and powerful force. Poseidon could be teaching Percy about the importance of all sea life along the way.
Well, perhaps in the fanfic, Percy is wrongly accused of a crime by Zeus. He then has to go on the run, all the while trying to clear his name. Along the way, he teams up with some unlikely allies, like a group of nymphs who have their own reasons for helping him. As he's on the run, he uncovers a conspiracy within the Olympian council that could change the fate of the demigod world forever.
A fanfiction could be about a competition among Zeus, Poseidon and Hades, and Percy has to be the judge. The competition could be something like who can best help a small, struggling mortal town without using their full power. This would show a different side of the gods and also test Percy's ability to be fair and objective.
One idea could be Percy having to prove himself to Zeus. Since he's his son in this fanfiction, Zeus might be overly critical. Percy could go on a quest to retrieve a powerful artifact that was once Zeus's but was lost. Another plot could involve Percy's relationships with other demigods changing. They might be jealous or in awe of his new status as Zeus's son.
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.