It could be that Hermione feels overshadowed in general. Harry is already famous in the wizarding world, and now if he's also doing well academically, she might worry that she's becoming less important. Also, she might be afraid that Harry is getting all the attention from the teachers, especially those she really respects, like Professor McGonagall.
One reason could be that Hermione has always been the one to help Harry and Ron with their studies. Now that Harry is getting good grades on his own, she might feel like she's losing her role in their group. Also, Hermione might be comparing herself to Harry not just in terms of grades but also in terms of how others perceive them. Harry is often seen as the hero, and if he's also an academic success, she might feel left out or less special.
The jealousy in this fanfiction scenario can have a complex impact on their friendship. Hermione's pride in her academic achievements is a big part of her character. When Harry gets good grades, she might feel like she's losing her 'edge'. This could make her distance herself from Harry. But as the story progresses, they'll realize that they each have their own strengths and weaknesses. Harry's success in grades doesn't diminish Hermione's intelligence, and they'll learn to support each other again, strengthening their friendship in the long run.
One way to develop this in a fanfiction could be to show Hermione's inner thoughts. She's always been a top student, so seeing Harry get good grades might make her question her own intelligence. For example, she could start comparing their study methods. Harry might have a more intuitive approach while she's all about strict study schedules. This could lead to her feeling jealous and trying to outdo Harry in a friendly competition, which would add an interesting dynamic to the story.
One plot twist could be that Hermione's jealousy is actually part of a spell cast on her. An enemy of the trio wants to create discord between them, so they cast a spell that magnifies her normal competitiveness into full - blown jealousy. As the fanfiction unfolds, she starts to realize her feelings are not normal and with the help of her friends, she breaks the spell. Or perhaps, Harry's grades are part of a prophecy - related phenomenon. Hermione's jealousy then takes a backseat when they realize the greater implications of Harry's academic success in relation to the prophecy.
Perhaps there are situations where Hermione seems overly possessive. Like when it comes to group projects or activities, if she doesn't like it when others take Harry's attention away from her for too long. Harry could see this as jealousy. Also, it might be related to her competitive nature. If she sees someone else getting praise or attention from Harry that she thinks she deserves more, it could lead Harry to think she's jealous.
Harry might be really confused at first. He doesn't understand why Hermione is acting so strange. He might try to talk to her about it, but if Hermione is being stubborn, he could get frustrated. He could also be a bit oblivious and just think Hermione is being overprotective as a friend.
One possible reason could be that Harry has some secret study techniques he hasn't shared. Maybe he has a better understanding of practical magic which is more emphasized in the grading system in this fanfic.
In these fanfictions, Ron's jealousy is portrayed in various ways. Sometimes he'll try to interfere with Harry and Hermione's time together. He might create small misunderstandings between them on purpose. Other times, he'll show his jealousy more subtly, like by looking sad or disappointed when they share a private joke or moment. His body language can also give it away, like crossing his arms and frowning when they are being friendly with each other.
Perhaps Harry was trying to hide from some danger. He knew that Hermione's place was one of the safest. So he transformed into his Animagus form and made his way to Hermione, and she took him in as a pet. In his animal form, he could stay close to her and keep an eye on things while remaining undetected by the source of the danger.
One possible reason could be that Dean is better at something that Harry secretly wishes he was good at. For example, if Dean is really popular among their peers and Harry feels overshadowed. Another reason might be related to a girl they both like. Maybe the girl shows more interest in Dean, and Harry can't help but feel jealous.
Often, Ginny will try to insert herself between Harry and Hermione. She might constantly try to get Harry's attention when he's with Hermione or try to exclude Hermione from activities that involve Harry. In some fanfictions, Ginny might even spread rumors about Hermione to try and drive a wedge between her and Harry.