Well, it could be that Percy yells at Nico because he feels Nico is being too reckless in a dangerous mission. Maybe Nico is about to do something that could endanger the whole group, and Percy, being the protective type, loses his temper.
Perhaps Percy yells at Nico over a misunderstanding. Nico might have been doing something in secret that Percy misinterprets as being against their friends. For example, Nico could be communicating with some shady characters, but in reality, he has a good reason which Percy doesn't know yet.
It could also be that Percy has his own insecurities and takes them out on Nico. He might see Nico's growing power and popularity among some of the group members as a threat. So, in a moment of weakness, he yells at Nico, which then leads to a rift between them that needs to be mended later.
One possible plot could be that Percy has finally had enough of the gods' interference in his life and the lives of his friends. He might yell at them for their unfair treatment, like how they often use demigods as pawns in their games. Maybe he'll demand more respect for the sacrifices demigods make.
In a 'Percy and Nico are betrayed' fanfiction, perhaps they are betrayed by the gods. The gods, fearing their growing power, might spread lies about them among the demigods. Percy and Nico then have to fight not only against the false accusations but also the demigods who turn on them. They would have to find a way to clear their names and prove their loyalty.
In this fanfiction, perhaps Percy adopts Nico after Nico has been ostracized by the other demigods. Percy realizes that Nico needs a safe space. So he offers his home. As time passes, they start to understand each other better. Nico might open up about his past traumas to Percy, and Percy would use his own experiences to help Nico heal and feel like he belongs.
Well, perhaps Percy and Nico could be transferred to Hogwarts through some sort of magical accident. Maybe they'd have to deal with the different magical system there compared to their own world. They could make new friends among the Hogwarts students and get involved in the typical Hogwarts adventures like the Triwizard Tournament or dealing with a new dark threat.
Well, it could be that Nico has some dark plan. Maybe he believes Percy is the key to saving someone he loves in the Underworld. He might think that by kidnapping Percy, he can force Percy to use his powers to bring that person back to life or something like that.
Perhaps in the fanfiction, Nico has been tricked by an enemy. This enemy convinces Nico that Percy is a threat to their world. So, Nico decides to take matters into his own hands. Another possibility is that Nico's own internal demons, related to his past traumas and his complex relationship with the gods, drive him to see Percy as an obstacle that needs to be removed.
Perhaps it's a fanfiction focused on their relationships. They might form an unexpected bond in the story. Nico, who has often been a bit of an outcast, could find real friendship and acceptance from Percy and Thalia. They could start out on a simple quest, like finding a lost artifact, and during this journey, they learn more about each other and grow closer as friends.
Well, one possible plot could be Percy and Nico having to deal with typical high school problems like bullies. Percy might use his water powers in a discreet way to stop them. Nico could be the mysterious loner at first but then make some real friends as he shows his cool powers. And they might also have to hide their demigod identities from the normal students.
Well, it could be about Apollo's over - confidence. He might have boasted about his powers or achievements in a way that annoyed Artemis. In the context of the Percy Jackson universe, Artemis is very protective of her domain and those associated with her. If Apollo made a decision regarding something that was under Artemis' purview without consulting her, like interfering in the affairs of the hunters, Artemis would yell at him. Also, Apollo's past mistakes or actions that went against the values of the gods might be brought up by Artemis during her yelling.
The camp leaders might betray them. If there is a power struggle within the camp, and Percy and Nico are seen as threats to the current leadership's power, the leaders could set them up. They could make it look like Percy and Nico are breaking camp rules or endangering the other campers, which would lead to the rest of the camp turning against them.