One possibility is that they form an alliance. Since both are heroes in their own right, they could combine their skills. Percy with his water - controlling abilities and Perseus with his experience in slaying monsters like Medusa. They might go on a new adventure together, perhaps facing a threat that neither could handle alone.
You can start by looking on fanfiction websites like Archive of Our Own. It has a large collection of fan-made stories, and you're likely to find quite a few 'Percy Jackson Perseus Fanfiction' there.
A notable 'Percy Jackson Perseus Fanfiction' is 'Perseus' Legacy in Percy's World'. This one is interesting as it explores what would happen if Perseus' legacy had a more direct impact on Percy's life. It weaves in elements of Greek mythology in a fresh and engaging manner, making for a great read.
One common theme is the crossover aspect. Writers often combine the different universes, like having Percy Jackson meet characters from Avatar or Perseus. This creates interesting scenarios and new storylines.
It could be portrayed as a clash of two different hero archetypes. Percy, the modern - day demigod with a rebellious streak, and Perseus, the more classic hero. Maybe they meet in a dream - like realm first and then in the real world.
In this fanfiction concept, imagine Savitar being from a different dimension and accidentally stumbling into the Percy Jackson universe. He doesn't understand the rules at first. The demigods are initially scared of him because of his speed and strange powers. But Annabeth, being the smart one, figures out a way to communicate with him. Through their interactions, Savitar starts to question his own motives and actions, leading to a character arc where he may even end up helping the demigods against a greater threat.
Another option is to join fan communities on social media platforms such as Reddit or Tumblr. There are often dedicated groups or pages where fans share and recommend their favorite fanfictions. For example, on Reddit, you might find a subreddit for Percy Jackson or Avatar fanfiction, and people there can point you in the right direction.
Percy would likely be very critical of their lifestyle. He comes from a world where family is important and they support each other in the face of danger. The Dursleys, on the other hand, seem to shun anything out of the ordinary and are unkind to Harry. Percy might try to show them a different way of living, with more love and acceptance, though they probably wouldn't listen.
A typical scenario could be Percy seeking Poseidon's help. For example, if Percy is in a tough battle against a powerful enemy, he turns to his father. Another is Poseidon coming to Percy to give him a task, like protecting a certain sacred place in the ocean.
Well, they might start comparing their heroic deeds. Percy could talk about his adventures with the Greek gods and monsters in the modern world, like fighting the Minotaur in a New York museum. Theseus would probably share his own tales of slaying the Minotaur in the labyrinth long ago. They could also end up teaming up to face a new threat that emerges in the fanfiction world, perhaps a powerful new monster created by an angry god.