One idea could be that Percy Jackson is stuck in a time loop like in Groundhog Day. He keeps reliving the same day where he has to face a monster attack at Camp Half - Blood. Each time he relives the day, he tries different strategies to defeat the monster more efficiently and protect his friends better.
In this fanfic, Percy could find himself in a situation where he is the only one aware of the time loop. He decides to use this to his advantage to prevent a major disaster that is supposed to happen in the future. He tries to convince his friends about the impending doom, but since they don't remember the previous loops, they are skeptical at first. So he has to find ways to prove it while also trying to stop the disaster.
Maybe Percy wakes up one day and realizes that it's Groundhog Day, but in the world of demigods. He uses this repeating day to train harder, learn new combat skills, and also figure out a mystery that has been plaguing Camp Half - Blood. He could start by investigating some strange happenings around the camp that he never had time to fully explore before.
One idea could be that Cleopatra is actually a demigod in the Percy Jackson universe. Maybe she has some special powers related to water, like being able to control the Nile in a way that no one else can. This could tie into the Percy Jackson world where demigods have unique powers.
One great Percy Jackson and Groundhog Day fanfiction is 'Groundhog Day at Camp Half - Blood'. In it, Percy wakes up to the same day over and over again at camp. It's really interesting to see how he tries to figure out what's going on and how he uses his demigod powers in different ways each day to break the cycle. It also has some really funny moments with his friends like Annabeth being confused by his strange behavior.
One idea could be that Percy finds himself magically transported to Skyrim. He could use his water - based powers in the frozen landscapes, like creating ice bridges over rivers or using water currents to his advantage in battles against the various creatures in Skyrim.
A possible fanfiction could involve a crossover where some of the Avengers are sent to Camp Half - Blood. Imagine Tony Stark trying to figure out how the magic at the camp works while also being highly amused by the whole concept of demigods. Steve Rogers could bond with some of the more heroic demigods over their shared sense of duty. Meanwhile, Percy and his friends have to keep an eye on the Avengers to make sure they don't accidentally disrupt the delicate balance of the camp. And then, they all have to face a threat that targets both the Avengers and the demigods, like a group of villains who want to steal the powers of both.
Perhaps there's a plot where the dinosaurs are being used by an evil force. The evil force has found a way to control the dinosaurs and is using them to attack the demigod camps. Percy and his friends then have to figure out how to break the control and save the day. They might find out that the dinosaurs have a connection to an old Greek god or goddess that they didn't know about before.
One idea could be that Percy Jackson discovers a hidden Cybertronian relic. This relic has the power to control water in a way that even Poseidon's trident can't. The Autobots and Decepticons are both after it. Percy has to team up with the Autobots to keep it out of the Decepticons' hands and also figure out how it relates to his world of Greek gods.
In a fanfiction, perhaps the gods in the Percy Jackson universe are aware of Cthulhu as an ancient and powerful being from another realm. They send Percy on a quest to learn more about Cthulhu's weaknesses in case he ever wakes up fully. Percy teams up with some of his demigod friends and they encounter all sorts of Lovecraftian horrors along the way. They soon realize that Cthulhu's power is far greater than anything they've ever faced and they have to rely on their wits and some newfound magic to survive.
In a fanfic, Percy could be a new student at the academy, but with his demigod powers. His water - controlling abilities would be quite a shock to the vampire and monster students. There could be a plot where some of the vampires want to use Percy's powers for their own gain, leading to an exciting adventure of Percy trying to outwit them.
In this fanfiction, the gods in Percy Jackson's world are intrigued by Poison Ivy's power. They bring her to Olympus to study her. Percy is assigned to be her guide while she's there. Along the way, they discover that there are similarities between the magic in Poison Ivy's world and the divine powers in Percy's world. They start to experiment with combining their powers, like Percy using his water powers to help Poison Ivy's plants grow in unexpected ways, and Poison Ivy using her plants to create shields for Percy during his training sessions.
One idea could be to have Percy Jackson end up in Middle - earth. He could use his water - related powers to help in battles against Sauron's forces, like using water to put out dragon fire. His demigod skills would be a new element in the LOTR universe.