One idea could be that Percy and his friends find themselves in the Star Wars universe. Maybe they land on a planet that's rich in water, like Naboo. Percy could use his water - controlling abilities to help the locals against some kind of threat, like the Trade Federation. Meanwhile, the Jedi could sense the different kind of power Percy has and be both intrigued and cautious.
Another idea is that Sophie Foster from KotLC travels to the Percy Jackson universe. She could be mistaken for a demigod at first. She would have to learn about the Greek gods and monsters. Her telepathic abilities would be really useful in the Percy Jackson world. For example, she could communicate with some of the monsters to find out their plans. And Percy and his friends would help her understand this new and dangerous world.
Annabeth, with her intelligence and strategic mind, could become an advisor to the Rebel Alliance. She could help them plan battles and fortifications, much like she did in the Percy Jackson series against the Titans. Grover, being a satyr, could befriend some of the more nature - based species in the Star Wars universe, like the Ewoks. He could communicate with them and help them understand the threat that the Empire poses to their way of life.
One place to find good fanfiction for this combination could be Archive of Our Own (AO3). Just search for 'Percy Jackson and Star Wars Rebels' there. You'll likely come across various creative stories that blend the two universes, like ones where the characters from Percy Jackson somehow end up in the Star Wars Rebels' galaxy and have to adapt to the new setting and its challenges.
One interesting plot element is the clash of different power systems. In Percy Jackson, we have demigods with their own unique powers based on their godly parentage. In Star Wars Rebels, there's the Force. So, when these two collide in fanfiction, it creates a really exciting dynamic. For instance, a demigod might be confused by the concept of the Force or try to use their own powers to interact with it in strange ways.
One possible fanfiction could be about a Sith Lord from Star Wars ending up in the Naruto universe. Maybe he tries to use the Force to control the chakra, but finds that it's a completely different power system. He could then form an alliance with some of the villains in Naruto, like Orochimaru, who are also interested in power and dark arts.
One great Percy Jackson and Immortal crossover fanfiction is 'The Immortal Demigod'. In this story, Percy discovers he has an immortal side due to some ancient magic. It's full of action and interesting character interactions. The author does a great job of blending the two worlds together.
One way could be to have Percy Jackson's powers of being a demigod interact with the superpowers of the Avengers. For example, his ability to control water could be used in a joint mission with Thor's lightning powers. Maybe they are facing a common enemy that can only be defeated by combining their unique skills.
Yes, there are quite a few out there. Some fanfictions combine the unique elements of the Star Wars universe like the Force, lightsabers, and the epic space battles with the ninja skills, chakra systems, and unique characters from Naruto. For example, you might find a story where a Jedi has to learn ninja techniques or a ninja discovers the power of the Force. It's really interesting to see how different authors blend these two very different but equally fascinating worlds.
In a Naruto and Percy Jackson crossover fanfiction, the characters could have some really interesting interactions. For example, Naruto's ninja skills like shadow clones could be compared to Percy's ability to summon water creatures. Maybe they would team up to fight a common enemy that threatens both their worlds, like some sort of mythical - ninja hybrid monster. Also, Naruto could learn about Greek mythology from Percy and vice versa, leading to some funny and unexpected cultural exchanges.