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.
In this kind of fanfiction, often the jealous demigods might be jealous of Percy and Annabeth's relationship or their status as heroes. Maybe they're jealous of Percy's powers over water or Annabeth's strategic mind. This can lead to all sorts of conflicts, from petty rivalries to full - blown battles.
In many fanfictions, Annabeth might be jealous of Percy because of his popularity or his close relationships with other characters. It could also be due to his natural talent in certain areas that overshadows her own at times.
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.
Communication is key. They need to sit down and talk about their feelings. For example, Percy could tell Annabeth that he's only being friendly with the new demigod who seems to like him, but his heart is with Annabeth. Annabeth could then share her insecurities. Another way is through a shared adventure. If they go on a quest together where they have to rely on each other, they'll realize that their relationship is stronger than any jealousy - inducing situation. They could also be given a task by Chiron that forces them to work together and face their jealousy head - on.
One possible reason could be Percy's natural leadership skills. He often takes charge in dangerous situations and gets a lot of attention for it. Annabeth might be jealous because she also wants that level of recognition.
They could face challenges like being sabotaged during quests. For instance, a jealous demigod might mess with their supplies or give them false information about the mission.
The jealousy can initially strain their relationship. Percy's jealousy might make Annabeth feel smothered or like he doesn't trust her. For example, if Percy is jealous of Annabeth's friendship with a male demigod, he might act coldly towards her, causing her to be confused and a bit hurt.
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.
It could be new girls who come into the camp. They see Annabeth's position and all she has achieved, like her close friendship with Percy and her role as a leader, and they become jealous. Maybe some minor characters who have always been in the background and feel overshadowed by Annabeth.