You could write a fanfic where Percy gets caught in a power struggle between two Olympian gods, say Zeus and Hades. This could involve Percy having to make difficult choices to keep the peace among the gods. Or perhaps a fanfic about Percy and Artemis, where Percy has to assist Artemis in protecting a sacred grove from some dark force. This would bring out the different aspects of their personalities and powers.
One idea could be to explore the relationship between Percy and Apollo in a modern setting. Maybe Percy has to team up with Apollo for a mission, and during the process, they learn from each other's strengths and weaknesses. Another idea is a story about Percy and Poseidon's father - son relationship within the context of the Olympian world, like Percy trying to prove himself to his father in a new way.
First, decide which Olympian god you want to focus on in relation to Percy. Then, think about the setting. It could be in the Camp Half - Blood, or in one of the Olympian realms. Next, come up with a basic plot like Percy needing the god's help for a quest or the god asking Percy for a favor.
One idea could be Percy discovers a new power related to the elements and has to learn to control it quickly to save his friends from a powerful enemy. For example, if he gains the ability to manipulate fire, he might accidentally set things on fire at first.
A cool plot could be that the God of Death has gone rogue and is starting to take souls before their time. Percy, with his friends, has to find a way to stop the god. They would have to search for ancient artifacts that can control or at least influence the God of Death's actions. They'd face many challenges, like traps in the Underworld and battles with deathly minions.
Maybe in the fanfic, Percy teams up with some unexpected allies, like a group of minor gods who also feel threatened by the more powerful gods' actions. Together, they form a plan to slay a corrupt major god, which involves traveling to different realms and facing various mythical creatures along the way. The story could explore themes of friendship and betrayal as they work towards their goal.
Another possibility is a story where the gods from Percy Jackson's world interact with the gods in the God of War universe. The gods in Percy Jackson are more involved in the lives of their demigod children, while the gods in God of War are often more distant and feared. This could lead to some interesting power struggles and misunderstandings. For example, Zeus in Percy Jackson might have a very different relationship with his children compared to Zeus in God of War.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
One idea could be that Percy has to hide his Titan heritage from the other demigods at Camp Half - Blood. He discovers new powers related to his Titan side that are different from his godly powers. For example, he might have the ability to control certain aspects of nature in a more primal way compared to his Poseidon - related powers.
One idea could be a fanfic where Sally tells Percy stories about his father from her own perspective before he knew the truth. It would give a deeper look into their relationship and how Sally coped with the knowledge of Poseidon.
One idea could be exploring the lives of the children of the original demigods. For example, how they deal with the legacy of their parents' great deeds and also face new threats. Another could be a time - travel fanfic where a modern - day demigod goes back in time to the era of the first Percy Jackson adventures and has to interact with the younger versions of the characters.
Another interesting concept is a crossover of the storylines. The prophecy in Percy Jackson could somehow be related to the events in Undertale. For instance, the hero's journey in both worlds might be intertwined, with Percy and Frisk having to work together to save both their universes from a common threat.