One idea could be that Percy gets sent on a quest in a different realm while Annabeth is stuck in Camp Half - Blood dealing with internal camp issues. This separation could lead to both of them growing individually. Percy might learn new powers or make new allies in the other realm, and Annabeth could strengthen her leadership at the camp.
Maybe there's a magical accident that causes Percy to be lost in time, and Annabeth has to search for a way to bring him back. In the meantime, Percy is trying to survive in a different era, facing challenges that are unique to that time period. This would create a lot of tension and longing between them.
Another fanfic scenario could be that an enemy devises a plan to split them up. They are separated on different islands. Percy has to deal with sea monsters and figure out how to escape his island, while Annabeth uses her wits to solve the puzzles on her island and find a way back to Percy.
A simple plot could be that they are separated by a powerful spell. Percy is on one side of a magical barrier that he can't cross, and Annabeth is on the other. They can see each other but can't reach out. This would force them to communicate in other ways, like through telepathy if there's some kind of magic involved. It could also lead to them finding ways to break the spell from their respective sides.
Percy might be really depressed at first. He would constantly think about Annabeth and the times they had together. He might isolate himself from his friends for a while, just sitting by the water and reminiscing.
Another idea is that they are rivals in winning the favor of a powerful but mischievous god. The god sets tasks for them, and whoever completes the most tasks successfully will get a special reward. Percy's courage and Annabeth's wisdom are put to the test. This rivalry might also test their friendship as they are tempted to use underhanded tactics against each other but ultimately realize the value of their bond.
One idea could be a fanfic where Percy and Annabeth go on a new adventure together, facing a powerful new monster that has emerged in the world of the gods. They have to use their combined skills and knowledge to overcome it.
One possible reason could be a misunderstanding. Maybe Percy does something that Annabeth misinterprets, leading to a rift between them. For example, Percy might make a decision during a battle that Annabeth thinks is too risky and endangering others, and this causes a big argument that results in their separation.
The fanfic could be about Percy and Annabeth's kids participating in a friendly competition within the camp. It's a series of challenges that test their physical strength, strategic thinking, and teamwork. Through this competition, they learn more about their own abilities and the importance of working together, while also having some fun rivalries with other demigod kids.
A great plot idea is that the child has a special connection to the sea, like Percy, but also has Annabeth's wisdom. So they use this combination to solve a mystery that has been plaguing Camp Half - Blood for years. For example, the mystery of why some demigods' powers are fading. Another could be that the child gets sent back in time and has to interact with their parents when they were younger. This could create some really interesting situations and challenges for the child.
One plot idea could be that they are on a dangerous underwater quest. Maybe they get separated from the group and have to rely on each other for survival. In a moment of relief after escaping a sea monster, they share an underwater kiss.
A possible plot could involve a magical tournament where Percy and Annabeth are on opposing teams. Their rivalry gets in the way at first, but as the tournament progresses and they see the real threats emerging, they start to cooperate in a more covert way to ensure the safety of everyone involved.
You could write a fanfic about Percy and Annabeth in the future, like when they are adults. They could be building a new Camp Half - Blood type of place for demigods all over the world. But there are those who oppose their ideas, and they have to deal with politics and power struggles, all while maintaining their relationship strong through it all.