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.
In 'Percy Jackson Goes to Goode' fanfiction, there might be a mysterious student who seems to know a lot about Percy's world even though they are human. This student could be a seer or have some other special ability that allows them to see the truth about Percy and the demigod world. They could either help Percy or cause trouble depending on their motives.
In this fanfiction, apart from Percy, we could see his friends from Camp Half - Blood like Tyson. Also, some of the teachers at Goode who might have a more significant role this time. There could be new demigods that Percy meets at Goode. And don't forget the gods or goddesses who might interfere in Percy's life at Goode in some way, for example, Poseidon could give Percy some kind of sign or power boost when he is facing a difficult situation at school.
One potential new character could be a scientist, Dr. Thompson, who is studying the strange phenomena in Alaska that are actually related to the magical world Percy is part of. He initially doesn't believe in the magic but as he witnesses Percy's powers, he becomes an ally. There could also be a group of Inuit shamans who have their own powers and traditions. They might initially be wary of Percy but then come to respect him and work together with him to solve a problem that is endangering both the magical and non - magical parts of Alaska.
In this fanfiction, perhaps Percy will make new friends at Goode who end up getting involved in his demigod world. There could be a plot where the school is in danger, and Percy has to use his powers and knowledge of the mythological world to protect it. Maybe he'll also have some interesting interactions with his teachers who suspect there's something different about him.
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.
He could interact with his old friends at Goode, like Rachel. She has a special connection to the demigod world, and their relationship could be further explored. Also, there might be new teachers or students that Percy meets. Maybe a new student who is actually a demigod in hiding too, and they start to figure out each other's secrets.
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 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 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 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.
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.