Well, Percy might be quite amused. He's used to all kinds of crazy adventures in his own life, and musical fanfiction could seem like an interesting new take. He might enjoy seeing how fans interpret his world through music and story in the fanfiction.
Percy Jackson's reactions to the musical fanfiction could be quite complex. Given his character, he is someone who has been through a lot in his own adventures. He might approach the musical fanfiction with a sense of curiosity. He would be intrigued by how the fans manage to translate his story, which is full of action, magic, and mythology, into a musical format. He may find some parts of it really cool, like the way the music might be used to enhance the mood of his battles or his relationships with other characters. At the same time, he might also feel a bit strange seeing his life being fictionalized in this way, but I think he'd eventually come to appreciate the love and enthusiasm that the fans put into creating these musical fanfictions.
Well, you could write a fanfiction where Percy gets transported to an alternate universe where the gods are different. Maybe they're more benevolent or more cruel. He would have to figure out how to survive in this new world. Also, a story about Percy having to train a new demigod who has powers that are completely opposite to his own could be really cool. It would be interesting to see how he adapts his teaching methods.
There could be a fanfiction where the characters from Percy Jackson attend the same high school as the High School Musical crew. Imagine Annabeth Chase joining the academic decathlon team with Gabriella Montez. It would be filled with both academic rivalries and new friendships, and of course, some elements of Greek mythology sneaking into the high school musical world.
First, think about how the two universes can blend. Maybe the setting could be a high school that has both normal high school activities like in High School Musical and also secretly has demigods like in Percy Jackson. Then, pick characters from both. For example, you could start with a plot where Percy has to learn to sing for a school event because of some magical mishap.
One great Percy Jackson and Groundhog Day fanfiction is 'Groundhog Day at Camp Half - Blood'. In it, Percy wakes up to the same day over and over again at camp. It's really interesting to see how he tries to figure out what's going on and how he uses his demigod powers in different ways each day to break the cycle. It also has some really funny moments with his friends like Annabeth being confused by his strange behavior.
One idea could be that Percy Jackson is stuck in a time loop like in Groundhog Day. He keeps reliving the same day where he has to face a monster attack at Camp Half - Blood. Each time he relives the day, he tries different strategies to defeat the monster more efficiently and protect his friends better.
Since Percy has a sense of humor, he'd probably laugh at the funny parts of the musical fanfiction and not be too uptight about any inaccuracies. He is also loyal to his friends and the world he knows. So if the fanfiction distorts that, he might not like it as much.