There could be a new oracle who is specifically attuned to Percy's 'son of fate' situation. This oracle might be a young demigod with unique powers that help Percy understand his fate better. Maybe they can see visions of the future that are directly related to Percy's journey.
A new antagonist could also be introduced. This could be a powerful demigod who is jealous of Percy's 'son of fate' status. They might try to undermine Percy at every turn, believing that they should be the one with such a grand destiny. This character could create a lot of conflict and action in the fanfiction.
There could be a character who is a mentor to Percy in understanding his devilish side. This character might be an ancient being with knowledge of both the divine and the demonic. For example, a fallen angel who has seen the rise and fall of many with such mixed heritages.
There could be a local guide in the place where Percy is exiled. This character could be an outcast from their own community and help Percy navigate the strange new land.
Perhaps some minor gods who have been overlooked in the past. They could see Percy's new status as the 'Son of the Universe' as an opportunity to gain more influence and decide to ally with him. For example, the god of small rivers or the goddess of wildflowers.
A young demigod who has the power to communicate with the spirits of the monsters. This character could help Percy understand the motives of the monsters better and maybe find non - violent solutions to some of the conflicts.
One potential new character could be a selkie. Selkies are mythological creatures that can transform between seal and human form. This selkie could be an ally or a foe to Percy. Maybe there's a sea nymph who has a special connection to Percy's mother. She could show up to help Percy when he's in a tight spot. And what about a sea giant who was once an enemy of Neptune but now wants to make amends? He could be a very interesting addition to the story.
There could be a chaos spirit named Eris. Eris could be a mischievous character who both helps and hinders Percy on his journey with chaos. She might have the ability to shape - shift into different forms related to chaos, like a swirling vortex of dark energy.
There could be a time - keeper character. This person or being would be an expert in all things related to time and would either help or hinder Percy in his journey with his new power. Another new character could be a time - lost hero from the past that Percy accidentally brings forward in time.
There could be a new bully at Goode who targets Percy because he senses Percy is different. This bully might turn out to have some connection to the mythological world, like being a descendant of a minor god.
There could be a healer character. Since Percy is a broken hero, someone with the power to heal his physical or emotional wounds might be introduced. This character could have their own backstory and motives, perhaps being related to an ancient Greek deity of healing in a new and unique way.
A centaur who has lived in both the Roman and Greek territories. He could be a mentor to Percy, teaching him about the similarities and differences between the two cultures' ways of combat, magic, and survival. He could also have a lot of stories about the ancient times when the two cultures were more intertwined.