One great fanfiction idea could be a story where Zeus, Poseidon and Hades have to team up to face a common threat that is even more powerful than them. Maybe a primordial being awakens and they must put aside their differences. In this story, Percy could be the mediator between them, using his unique position as the son of Poseidon to try and keep the peace among the three powerful gods.
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.
A powerful Titan who sees Percy as a threat to his plans. Since Percy has the power of Zeus and Poseidon, he could potentially stop any chaos the Titan wants to create. The Titan might try to turn Percy's friends against him or find a way to strip him of his powers.
Well, if Percy was more powerful, he could act as a stronger mediator between Zeus and Poseidon. He might be able to force them to face their issues more directly. For example, he could use his increased power to create situations where they have to work together, like in the face of a new and extremely powerful enemy. This could lead to a begrudging respect between the two gods and a shift in their relationship from one of constant bickering to a more cooperative one, at least when Percy is around.
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 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.
Another possibility is that Percy discovers some long - forgotten weakness of Zeus. In the world of fanfiction, the author could create a scenario where Percy stumbles upon an ancient prophecy or a hidden secret about Zeus. This knowledge could give Percy the upper hand. He could then use his wits and his powers to exploit this weakness and defeat Zeus.
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.
In fanfiction, their relationship could be developed by having Poseidon be more involved in Percy's daily life. Instead of just popping in during big events, he could be there for the small things too. For instance, helping Percy with his schoolwork that involves marine biology. They could also have a project together like building a new safe haven for sea nymphs. Through this, they would bond over creating something positive. Also, Percy could start to take on some of Poseidon's responsibilities in the ocean, with Poseidon guiding him. This would not only strengthen their bond but also show Percy growing into his role as Poseidon's son.
One interesting fanfiction could be about Percy Jackson's adventures that are more closely tied to his relation as Zeus's grandson. Maybe he discovers some hidden powers that are passed down only through the Zeus lineage. He could face challenges where his Zeus - related powers are both a blessing and a curse, like when he has to control excessive lightning powers during a battle with a powerful monster.