Percy Jackson himself is extremely popular. He's the main character of the original series, so many fanfictions revolve around him having new experiences or facing different challenges.
Some fanfictions in the Percy Jackson Archive focus on the relationships between the characters. There could be a story about Annabeth and Percy having a big argument that leads to them exploring their own individual strengths and weaknesses separately for a while. Then, through a series of events, they come back together stronger than ever.
Percy himself is of course a very popular character in this type of fanfiction. Since it's about his journey in the past, he's the central figure. Another popular character is Annabeth. Fans often write about her either accompanying Percy in his time - traveling adventures or being the one waiting for him back in the present while he's in the past. And then there are the gods. Zeus, Poseidon and Athena are often included as they play important roles in Percy's past - related stories.
Percy Jackson himself is often a central character in these fanfictions. His powers and his journey as a demigod make him a natural focus. Annabeth Chase is also popular as she brings her intelligence and strategic thinking to the stories. Grover could be another popular character, especially if the fanfiction involves exploring new areas in Canada, as his nature - related abilities can come in handy.
Grover often appears in fanfiction as well. His loyalty to Percy and his own unique abilities as a satyr can be used in really interesting ways. For example, a story could revolve around Grover's search for a new type of magical plant that could save Percy from a deadly curse.
Obviously, Percy Jackson is a very popular character in this type of fanfiction as the concept often revolves around her in a futa form. Annabeth Chase is also popular as she is Percy's main love interest in the original series, and in the fanfiction, their relationship can be explored in new and different ways.
Percy himself is obviously very popular. After all, it's his series. Annabeth is also a fan favorite, as her intelligence and strong will make for interesting storylines. Nico di Angelo is quite popular too, especially when his powers and his somewhat dark nature are explored in fanfiction.
Annabeth Chase is also a favorite. Her strategic mind makes her a key player in the capture the flag scenarios. She can come up with brilliant plans to outmaneuver the other teams, like setting up elaborate traps or diversionary tactics.
Percy Jackson himself is of course very popular. His friends like Annabeth Chase also often appear. Grover could be there too, still being Percy's loyal friend. New characters might include college professors who turn out to have some connection to the world of mythology, like a history professor who is secretly a descendant of a minor god.
Grover can also be quite prominent. His loyalty to Percy remains a key factor. In some fanfictions, his connection to nature might be enhanced to better support Percy in his overpowered adventures. For example, he could be able to communicate with more powerful nature spirits to assist Percy in battles or quests.
One popular original character is often a new demigod who is related to Percy's family in some way. For example, a cousin who has a unique power that helps Percy and his family in their battles. This character adds a fresh perspective to the family's adventures.