They might start with some mutual suspicion. Percy would be cautious around Thor as he's a very powerful being from a different mythology. Thor might see Percy as a bit of an oddity at first. But then they could start to exchange stories about their adventures. Percy could tell Thor about his battles with the Titans, and Thor could share his tales of fighting giants. This would lead to a newfound respect between them.
In the realm of fanfiction and crossovers, it can be considered normal. Fanfic often plays with different universes colliding, so Thor being interested in a Percy Jackson fanfic is just part of the creative and often wacky world of fan - created stories.
In a fanfic where Percy Jackson meets Thor, there would be a clash of cultures as well as powers. Percy comes from a world of Greek mythology and Thor from Norse mythology. They might initially misunderstand each other's ways. However, once they start communicating, they could find common ground. Their powers could interact in unique ways. Percy's water powers could potentially cool down Thor's overheated hammer or something like that. And together they could create a whole new style of combat that combines the best of both their abilities.
One great Percy Jackson Thor fanfic is 'The Gods' Alliance'. It combines the worlds of Percy Jackson and Thor in a really interesting way. The characters interact in a way that feels both true to their original personalities and also creates new and exciting storylines. Another one could be 'Percy and Thor: A Meeting of Heroes' which focuses on a chance encounter between Percy and Thor and how they deal with the differences in their powers and cultures.
The plot could also involve Thor being curious about the demigod world. He might have heard tales of Percy's adventures and wants to meet him to learn more about how demigods operate, their powers, and their training. It could be a kind of cultural exchange between the Norse and Greek mythological worlds.
Another possibility is that during a quest, Percy finds himself in a place related to Thor's history. It could be an old Norse temple or a realm connected to Thor. There, he discovers hidden records or runes that point to his relation to Thor. This discovery would not only shock him but also open up new storylines such as him exploring his Norse heritage along with his Greek demigod side.
A simple plot could be that Percy discovers a way to enter the world of Thor. Once there, he tries to prove himself worthy to lift Mjolnir. Along the way, he teams up with Thor and the other Asgardians to fight off a new threat that endangers both his world and Asgard.
Well, perhaps Percy admires Thor's strength. Thor is a very powerful character in the Marvel universe, with his hammer and lightning powers. Percy might be drawn to his heroic deeds and his god - like status, which could be really exciting to explore in a fanfic.
In most Percy Jackson canon, there is no relation to Thor. However, in fanfiction, anything can be possible. It could be that the author has created a unique crossover where Percy Jackson has some connection to being the heir of Thor, perhaps through some magical or divine intervention that the fanfic writer has dreamed up.
Fanfiction.net is also a good place to look. There are many Percy Jackson fanfics, and although it might take some searching through the different categories and using relevant keywords like 'Thor' and 'meet', you could come across what you're looking for.