Perhaps it's a love story. If Percy is female in this fanfiction, she might fall in love with a character that she had a different relationship with in the original story. For example, if in the original there was a friendship, now it could be a romantic relationship. She could also be on a quest to find her true identity, being a female in a world that perhaps expected her to be male based on the original story.
One possible story could be that Percy, as a female, is leading a rebellion in a dystopian world that was inspired by the original story she is from. She uses her unique female perspective and skills to gather allies and fight against an oppressive regime. Another could be that she is a detective - like figure in a mystery set in the same universe as the original, but her female identity gives her different insights and ways of approaching the mystery compared to a male Percy would have.
In some fanfictions, Percy might be betrayed because of a prophecy that is misinterpreted. People think he will bring doom, so they betray him. It could also be that a powerful enemy manages to manipulate those around Percy, turning them against him by spreading lies about his intentions.
One possible story could be that Percy Jackson discovers a hidden Norse artifact while on a quest in the Greek world. This artifact makes him curious about Norse gods and he starts to study them. Another could be that he meets a demigod from a Norse - inspired camp and through their friendship, he becomes a fan of Norse gods.
One possible plotline could be that Percy has been betrayed by his closest friend. Maybe this friend revealed a big secret of Percy's, and now Percy feels isolated and heartbroken. He might start to question his relationships and his place in the world.
One possible plotline could be Percy's friends trying to break him out. They might have to overcome various obstacles like guards, traps, and security systems within the prison.
One possible plot could be that Annabeth is under some kind of mind control. Maybe a powerful enemy has taken over her mind, forcing her to turn against Percy. Another could be a misunderstanding. For example, she might think Percy has betrayed her or their friends in some way, leading to a tragic confrontation.
One possible storyline could be that Percy is tricked into betraying Tartarus by some dark force. Maybe they use his friends as hostages or manipulate his mind. Another could be that Percy believes he's doing the right thing in betraying Tartarus, but later realizes it was a huge mistake and has to face the consequences. For example, he might face the wrath of Tartarus' minions or lose the trust of his allies.
Well, perhaps in the fanfiction, Annabeth betrays Percy's trust in a relationship way. She could start seeing someone else and use Percy's secrets against him to make herself look better in front of the new person. Or she might side with a group that Percy is against, believing their lies and false promises over Percy's warnings. This could lead to Percy feeling completely alone and having to find new allies.
One possible scenario could be that Percy uses his water powers in a very unique way. Maybe he combines the power of the ocean with some sort of ancient magic he discovers to defeat Gaea. He could summon a massive tidal wave that not only physically overwhelms Gaea but also disrupts her connection to the earth.
Another plotline could involve Percy making new friends in the navy. These friendships could be tested during dangerous missions or when faced with internal conflicts within the naval unit.
Well, one scenario could be that Percy is bullied in school. Maybe the bullies pick on him for being different, like if he has some unique abilities or is just not as popular. Another situation could be that he's bullied in a new environment, like a summer camp, where the other kids don't accept him at first. It could also be that the bullies target Percy because of his family background or something that makes him stand out in a way they don't like.