Well, it depends on who's calling. If it's Tony Stark, for example, Peter would be super excited and might not be able to hide it. He could try to come up with some lame excuse to leave the class, like saying he has a stomachache. But the teacher might not believe him. And his classmates would be curious about who's on the other end of the call.
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.
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.
Well, he might get in trouble with the teacher. Teachers usually don't like students getting phone calls during class. So, the teacher could take his phone away and give him a detention.
In a fanfiction scenario, Peter Parker might be using his phone in class to check on the news about any recent crimes in the city. His friends notice him being distracted and start to tease him. However, little do they know that he's actually looking for signs of trouble so he can swing into action as Spider - Man right after school.
He could be using his phone to track a villain's movements. Maybe he installed some special app on his phone that can detect unusual energy signatures. So while the teacher is droning on about history or math, Peter is secretly following the path of a super - villain who is on the loose in the city.
Peter could get a dog. A loyal dog would be a great companion for him, following him around during his daily life and even being a sort of sidekick. It could sense danger and bark to alert Peter when something was wrong.
One idea could be that Peter Parker gets a prosthetic after a particularly dangerous battle with a villain. Maybe his leg is severely injured and he has to adapt to the new prosthetic while still maintaining his superhero duties. He could struggle at first with the balance and movement, but with his determination, he eventually masters it and even modifies the prosthetic to have some special features like enhanced jumping ability.
It could be a vengeful criminal that Spider - Man has put away in the past. This criminal has spent years in prison plotting his revenge and finally gets the chance when Peter is vulnerable. Maybe he manages to ambush Peter in an alleyway while he's on his way home from school or work.
Peter can be developed by showing his struggle to balance his normal student life in the Zoom class with his superhero duties. For example, he might be constantly distracted during class because he's worried about the next bad guy he has to fight. Also, his interactions with classmates during Zoom calls can show his growth as a person. If he's usually shy but has to speak up to defend someone from a bully during a call, it shows his courage.