One plot could be Percy seeing Annabeth spending a lot of time with another demigod on a quest. He gets jealous and starts acting strange around her. This could lead to some misunderstandings between them until they finally talk it out.
A possible plot is that a new camper at Camp Half - Blood shows an interest in Annabeth. Percy, being the possessive type, gets jealous. He starts to follow Annabeth around more, which annoys her at first. But as the story unfolds, they realize their feelings for each other are deeper than they thought and Percy's jealousy was just a sign of his deep love for her.
One interesting plot could be a quest where Percy, Rachel, and Annabeth have to work together to retrieve a powerful artifact. They might face various monsters and challenges along the way, and there could be some tension between Annabeth and Rachel as they both have feelings for Percy.
In some fanfictions, they could be studying in a magical library where the books come to life. This would add an element of adventure to their study sessions as they have to deal with the chaos caused by the animated books while still trying to study.
Another plot could be Aphrodite giving Annabeth a special charm that makes her irresistible to Percy, but in a way that causes chaos because Percy can't think straight. And Annabeth has to figure out how to break the spell without ruining their relationship.
In some fanfictions, the plot could be that Percy and Luke are in a battle of wits over Annabeth. For example, Luke uses his charm and knowledge of ancient lore to try and win her over, while Percy uses his loyalty and selfless acts. Or perhaps there's a plot where Annabeth is in danger, and Percy and Luke have different ideas on how to save her. Percy might want to rush in and fight, while Luke thinks a more strategic approach is needed, causing conflict between them.
One interesting plot could be Percy and Annabeth teaming up for a school project. They might face challenges like different study habits but in the end, they learn to work together and their relationship grows deeper. Another could be Percy getting into trouble with a school bully and Annabeth using her wits to get him out of it.
In some fanfictions, their summer love could be tested. For example, a new camper arrives at Camp Half - Blood who seems to have a connection with one of them. This creates jealousy and tension, but in the end, their love overcomes it all as they realize how much they truly mean to each other. They might have a big fight and then a really emotional reconciliation.
One possible plot could be that in the fanfic, Jason is jealous of Percy's natural leadership skills. Percy always seems to know what to do in a crisis, and the other demigods look up to him. Jason, on the other hand, feels like he has to constantly prove himself. So, he starts trying to outdo Percy in every mission, which leads to some tense and exciting situations. For example, they might both be trying to solve a mystery at Camp Half - Blood, and Jason's jealousy causes him to take unnecessary risks just to show he's better than Percy.
One idea could be that a new demigod arrives at Camp Half - Blood. This new demigod is really good - looking and shows a lot of interest in Percy. Annabeth gets jealous seeing them together all the time, like during training sessions or at the campfire. Another plot could be that Annabeth has to work closely with an old acquaintance on a quest, and Percy gets jealous because he feels left out and he's not sure about this acquaintance's intentions towards Annabeth. A third plot could be that in a school setting outside the camp, Percy is getting a lot of attention from mortal girls because of his heroic looks, and Annabeth has to deal with her jealousy while also trying to keep their demigod world a secret.
One more plot idea could be that Percy and Annabeth are somehow affected by the dark magic of Tartarus. It changes them in some way, either physically or mentally. They then have to deal with these changes while still trying to escape. This could lead to some really intense internal and external conflicts as they struggle to stay true to themselves and also find a way out of Tartarus.
Well, in many Percy - related fanfictions, if we consider Grover as Annabeth's friend, he might be jealous of Percy because Percy often gets more attention or seems to be more in the spotlight. Percy has a lot of heroic moments and is the son of Poseidon which gives him a certain status, and Grover might feel overshadowed at times.