There's a chance it's a mysterious figure who has some sort of mission or task for Percy that can't wait until after class.
Maybe it's a family member. For example, his sister could be calling because she needs his help with something urgent at home.
It could be his friends from his secret group. They might be in some kind of trouble and need his help right away.
There's also a chance that it could be a new superhero or villain. Maybe a new hero wants to team up with Spider - Man or a villain is taunting him, starting a new plot in the fanfiction world. This would create an exciting situation for Peter to deal with while trying not to blow his cover in class.
Maybe Percy gets in trouble for answering the call during class. It could disrupt the whole class and the teacher might scold him.
There's also a possibility that it's Trish. She could be calling to warn Dante about a new threat that she has discovered. Dante would trust her information and start to make preparations to face this new danger.
Perhaps it's his best friend who has some juicy gossip to share. But it's really bad timing as he's in class. His friend might not be aware of his class schedule.
Perhaps it's a gift from his father, Poseidon. Since Poseidon has control over the sea and all things related to water, he might have some connection to a power that gives Percy wings, like as a way to help Percy reach new heights both literally and metaphorically.
Maybe it's an ancient and powerful entity that has been awakened. Percy might be in the wrong place at the wrong time and this entity, seeing Percy as an intruder or a potential disruptor of its slumber, decides to seal him away using its otherworldly powers.
Fans of the original story or series that Percy and 'the hunt' are from would likely be interested. They might be drawn to this fanfiction if they enjoy exploring different and unexpected plot twists.
His best friend could be one of the main characters. They would likely be very concerned and play a big role in his recovery.
One challenge could be that the connection between them is being blocked. Maybe some dark magic or a powerful enemy has created a barrier. So Percy has to find a way to break through this block just to get his call for help to Poseidon. Another challenge might be that Poseidon is preoccupied with his own problems in the underwater world, like dealing with a rebellion among his own sea creatures. So Percy has to convince Poseidon that his situation is also important.