Well, the plot could be centered around Percy's attempts to bridge the gap between his father Poseidon and his grandfather Zeus. There have always been tensions between the two gods. Percy, using his unique position, tries to bring peace. But there are forces at work, like some rogue demigods who don't want peace between the two powerful gods. They try to sabotage Percy's efforts, leading to a series of adventures and challenges for Percy.
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.
Well, one possible plot could be Percy discovering he's Zeus' brother in a very unexpected way. Maybe through some ancient prophecy that was long forgotten. He'd then have to deal with the power struggles within the Olympian family, as well as his own identity crisis. Another aspect could be his relationships with other demigods changing, as being related to Zeus is a huge deal.
Well, it could be about the daughter of Zeus trying to fit in at Camp Half - Blood. Maybe she has powers that are hard to control, like being able to summon huge lightning bolts at unexpected times. She might struggle with the expectations that come with being the daughter of the king of the gods.
A possible plot could be Percy discovers Zeus has been secretly plotting against some of the more powerful demigods. Percy then challenges Zeus to a duel of sorts, with the fate of the demigods at stake. If Percy wins, Zeus has to stop his plotting and give the demigods more freedom.
One possible plot could be Percy discovering his relation to Dumbledore. Maybe he starts having strange dreams or visions that lead him to the wizarding world. He then has to learn about his new family connection while also trying to keep his demigod identity a secret from most of the wizards, as they might not understand it.
Well, one possible plot could be that Percy discovers his new relation to Hephaestus later in his adventures. He might then start to have an affinity for creating and fixing magical items, which could be a new skill for him in battles against monsters. He could also meet other descendants of Hephaestus who teach him more about his heritage.
One possible plot could be that the entire Greek pantheon is thrown into chaos. Percy might be seen as a huge threat, and other gods and goddesses would either try to hunt him down or form alliances with him out of fear or a desire for power. Demigods would be forced to take sides, leading to massive battles among them.
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.
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.
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.