Well, in fanfiction, anything can be made possible. One way could be through some sort of magical or divine intervention. Maybe there's a god or goddess who manipulates fate so that Bella Swan and Percy Jackson are siblings. It could also be that their parents have some sort of hidden connection that was never revealed in the original stories. Another idea is that they exist in a different dimension where the rules of their respective universes are merged, allowing for such a relationship to occur.
Simple. In the world of fanfiction, the author can create a backstory. Maybe both Bella and Percy are descendants of an ancient and powerful being that spans across different mythologies. This being could have influenced their parents' lives in such a way that they became siblings. Or, the author could make it so that there was a mix - up in the magic that governs family ties in both universes. So, instead of being in their separate storylines, they are now related. Fanfiction gives the freedom to twist and turn the existing lore to create such interesting relationships.
In fanfiction, it might be possible if we consider a multiverse theory. There could be a universe where the Twilight world and the Percy Jackson world collide. Perhaps their parents met in a place that exists between the two fictional realms. For example, if there was a magical crossroads where people from different mythologies and stories can interact. Then, their parents could have fallen in love and had them as siblings. Also, some fanfic writers might play with the idea of time travel or alternate timelines to make this relationship work.
One way the storyline could be is that Percy uses his demigod powers to protect Bella from the various threats in Forks. For example, he could sense the presence of vampires and werewolves before Bella does and keep her out of harm's way. He might also introduce her to the world of Greek mythology, which would be a huge contrast to the world of Twilight she already knows.
Well, in fanfiction, anything can be possible. Maybe it could be some kind of multiverse concept where different fictional universes collide. The author might create a backstory that involves some powerful magic or a strange twist of fate that binds Bella and Loki as twins, despite coming from seemingly different fictional worlds.
One possible plot could be that Percy somehow ends up in the Twilight world. He meets Bella and they initially clash because of their different personalities and backgrounds. But as they face common threats, like a new type of monster that combines the elements of Greek mythology and the Twilight creatures, they start to fall in love.
Well, in fanfiction, anything can be possible. It could be a multiverse concept where different mythologies collide. Maybe there's some sort of magical or divine interference that links Percy Jackson, a demigod from Greek mythology, to Loki, a Norse god. Writers often use their creativity to bridge such seemingly impossible connections for an exciting and unique story.
They could go on a quest to find a magical object that has the power to balance the magic in both their worlds. Since Percy is used to dealing with Greek mythology - related quests and Bella has her own experiences in the Twilight world, they could combine their skills. For example, Percy's ability to fight monsters and Bella's immunity to some vampire powers could come in handy.
One possible storyline could be that Bella discovers her sisterhood with Jane and tries to use it to protect the Cullens from the Volturi. She might try to negotiate with Jane, using their family bond to sway her decisions regarding the Cullens.
Percy's relationship with Jacob could also be a key part of the story. They might initially be at odds because Jacob is a werewolf and Percy is used to dealing with different kinds of 'creatures'. But over time, they could learn to work together, especially if they both have Bella's best interests at heart. Percy's interactions with Bella herself would be a mix of brotherly love and trying to keep her out of supernatural trouble.
She might become more protective. As Silas's sister, she would have a natural inclination to safeguard him, which could make her more assertive.
A possible plotline could be that the Winchester sisters are magically transformed into Bella Swan right before a major event in the 'Twilight' series. They then have to quickly adapt to her life and relationships while also trying to figure out a way to get back to their own world. They might use their combat skills to protect themselves from the vampires and werewolves in a more aggressive way than Bella usually does.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.