Another way is through the reactions of other characters. If other characters seem to favor Percy more, it can fuel Annabeth's jealousy. She might see how others flock to Percy and feel left out or less important, which then intensifies her jealous feelings.
Often, it starts with small incidents. For example, Percy might get praised for a simple task that Annabeth thinks she could have done better. This builds up her jealousy gradually.
Often, it starts with small incidents. For instance, Bella might get praised in front of Lauren for something she did. This makes Lauren feel inadequate. Then, as the story progresses, more and more situations arise where Bella is in the spotlight and Lauren is left out. Like at a big event in the fanfiction, Bella is the center of attention while Lauren is just a bystander.
The fanfiction might develop it through relationships. Say, Jason becomes closer to a group of characters that Percy wants to be part of. Percy then feels left out and his jealousy towards Jason intensifies. There could also be public events where Jason is praised and Percy is not, which is a common way to build up this jealousy plot.
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.
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.
Another way it could end is that through the jealousy, Annabeth discovers new things about herself. She realizes that she has been taking Percy for granted in some ways. So, she works on herself and her relationship with Percy. Rachel may or may not still be in the picture, but Annabeth and Percy's bond becomes deeper and more understanding, with Annabeth no longer feeling jealous.
Annabeth might be annoyed. She's very perceptive, so she quickly realizes Jason's jealousy. She'll probably tell him directly to stop acting childish and respect her relationship with Percy.
Luke's jealousy can drive him to take actions that create conflict. He might try to undermine Percy's achievements or come between Percabeth. For instance, he could spread false rumors about Percy to turn others against him.
Often, she becomes overly possessive. If she sees Percy talking to another girl, she'll quickly insert herself into the conversation. She might put her arm around Percy or give the other girl a look that clearly says 'he's mine'. This possessiveness is a clear sign of her jealousy in the Percy Jackson fanfiction world.
The jealousy can create conflict. Jason might start to act out, causing rifts between himself and Percy or Thalia. This can lead to different story arcs, like a rivalry developing. For instance, he could try to undermine Percy's actions or try to get closer to Thalia in a way that seems forced, which drives the plot forward as other characters react to his behavior.