Since I don't have access to the 'percy is mad fanfiction', it's difficult to give a detailed account. However, generally speaking, if Percy is mad, the fanfiction could be exploring his emotions deeply. It might show how his anger affects his actions, decisions, and relationships. For example, if it's a fanfiction related to Percy Jackson, his anger could lead him to take risks he wouldn't normally take, or it could cause rifts in his friendships with Annabeth or Grover. It could also be a story about how he overcomes his anger and grows as a character.
Well, in many fanfictions, Percy might be seen as too ambitious and career - focused. He could have made choices that put his job at the Ministry above his family. For example, he might have supported Ministry policies that the rest of the Weasleys disagreed with, like their stance on Harry Potter or how they were handling the growing threat of Voldemort. This could lead to the Weasleys being mad at him for seemingly choosing the wrong side or not standing by the family values.
Well, in some fanfictions, Percy might be mad at Annabeth because of a misunderstanding. Maybe she made a decision without consulting him in a crucial situation regarding their adventures. For example, if she chose a path that put their friends in danger without his input, Percy could get angry.
One possible plot could be that Percy gets mad because his friends don't believe him about a new threat he has discovered. He might storm off and try to face the threat alone, leading to all sorts of dangerous situations.
One idea could be that the mad scientist discovers Percy's demigod powers and tries to replicate them in a lab - creating some sort of artificial half - blood. Another could be that the mad scientist is working for a Titan and is using his inventions to try and defeat Percy and his friends. Or perhaps the mad scientist has created a time - traveling device and accidentally sends Percy to a time when the gods were first born, causing all sorts of chaos.
One scenario could be that Annabeth accidentally revealed Percy's secret identity to someone he didn't want to know. This could put him in danger and make him furious with her.
Perhaps Percy forgets an important promise he made to Annabeth. In their relationship, promises are significant. If he fails to keep one, like a promise to help her with a project or be at a certain place at a certain time, Annabeth would surely be mad. It could also be that Percy accidentally breaks one of Annabeth's creations or possessions, which she holds dear.
Perhaps Percy made a decision without consulting Annabeth. In many fanfictions, Annabeth values being part of the decision - making process, especially when it concerns their relationship or a mission they're on. If Percy went off and did something like made a deal with a potentially dangerous character on his own, Annabeth would be furious.
Let's say Annabeth put Percy's friends in danger without his knowledge. Percy is very loyal to his friends, and knowing that Annabeth's actions could have hurt them would surely make him angry at her.
The Weasleys could also be the ones to reach out first. They might realize that Percy was in a difficult situation at the Ministry and that he didn't mean to cause them harm. So they forgive him and they all work together to face whatever threats are out there, like Voldemort's return.
It could be a new character, like a powerful wizard who has a grudge against Percy for some reason. Maybe Percy accidentally disrupted one of his spells, and the wizard is out to get him, which makes Percy mad.