Annabeth from Percy Jackson could be the most interesting. She's highly intelligent and strategic. In a crossover with Twilight, she would be the one trying to figure out how the vampires work and how to use their abilities to their advantage. She might also be a bit suspicious of them at first and would be constantly analyzing their every move, which could lead to some really engaging scenes in the fanfic.
Grover from Percy Jackson would also be a fascinating crossover. His connection to nature and his ability to sense things that others can't would be really cool in the Twilight world. He could befriend the werewolves because of their connection to nature as well. And his generally nervous but loyal personality would add a different flavor to the interactions in the Twilight world.
One idea could be that the demigods from Percy Jackson's world end up in Forks for some reason. Maybe they are on a quest that leads them there. And they cross paths with the vampires and werewolves from Twilight. For example, Percy could use his water powers to fend off some danger that the Twilight characters are facing, like a wildfire started by a vampire's power going out of control. This would create an interesting dynamic as the two different mythologies collide.
Percy himself would be really interesting. His carefree yet heroic nature in the world of Twilight would be a contrast. He'd be the one bringing his demigod powers and his sense of humor. Just think of him trying to make friends with the vampires and werewolves while still being true to his demigod self.
One great 'Percy Jackson Twilight crossover fanfic' is 'Twilight of the Gods'. It combines the mythological elements from Percy Jackson with the vampire - werewolf lore of Twilight in an exciting way. The characters from both universes interact in a really interesting plot that keeps you hooked.
Well, in a 'Percy Jackson and Twilight crossover fanfic', there could be a plot where the threat of a common enemy forces Percy's gang and the Cullens to team up. The demigods' skills in combat and their connection to the gods could be combined with the vampires' superhuman abilities like speed and strength. It could also explore how the different mythologies in both universes interact. Like, how would the Greek gods view the existence of vampires? And would the Twilight vampires be affected by the magic that exists in the Percy Jackson world?
Another great pairing could be Jacob and Grover. Jacob is a werewolf with a strong sense of loyalty and Grover is a satyr, always looking out for demigods. They both have a connection to nature in different ways. Jacob with his wolf form and Grover with his love for the wild. They could have some really fun adventures together as they explore both the Twilight and Percy Jackson worlds.
One possible plot could be that the Volturi from Twilight discover the existence of demigods from the Percy Jackson world. They see the demigods as a threat to their vampire supremacy. Percy and his friends have to team up with some of the more friendly vampires, like the Cullens, to fend off the Volturi. This would bring together the magic and powers of both universes in an epic battle.
The demigods have a variety of powers. Annabeth's strategic mind could be combined with Alice's ability to see the future. They could plan out battles or ways to avoid danger. If a demigod like Jason with his lightning powers teams up with the vampires, they could use the lightning to create distractions or even as a weapon against common enemies. The vampires' super strength and speed could also be useful in getting the demigods out of tight spots quickly.
Often, a main plot point is the meeting of the two sets of characters. For example, Percy and his friends might stumble into the Twilight world. Another common plot point is the clash of powers. Demigod powers like controlling the elements in Percy Jackson contrast with vampire and werewolf abilities in Twilight. Also, there could be a common enemy that forces them to work together, such as a new, powerful dark force that threatens both their worlds.
Percy Jackson and Thor would be an interesting pairing. Percy has his water powers and connection to the sea, while Thor has his lightning powers. They could have some really cool battle scenes together, like when they face a water - and lightning - based enemy. Also, they both have a bit of a sense of humor and a heroic nature, so they'd probably get along well.