Another possibility is that some minor characters from the original series get more spotlight in this fanfiction. For example, some of the campers at Camp Half - Blood could join Percy in his training. They might have different skills and personalities that add variety to the training sessions and the overall story.
In addition to Percy's usual friends, new characters might be introduced in this fanfiction. There could be a wise old trainer who has a mysterious past and imparts valuable knowledge to Percy. Or there could be a rival who challenges Percy during his training, pushing him to improve even more.
Obviously Percy himself is the main character. There could also be his friends like Annabeth. She might be supporting him in his training, or even training with him. Grover could also be involved, perhaps using his nature - related powers to help Percy in some unique training exercises.
His friends could be involved, like Annabeth. She might be mourning at the funeral and then be extremely surprised and happy when Percy shows up. Grover could also be there, and he'd probably be the first to give Percy a big, emotional hug.
Well, one interesting aspect could be how Percy overcomes his physical limitations. Maybe he discovers new training techniques that are unique to the fanfiction world. Another aspect could be the relationships he forms during his training journey. For example, he might meet a new mentor who helps him in ways his old friends couldn't.
There could be a rival within the family. Someone who wants Percy out of the way, perhaps for inheritance reasons or because they're jealous of Percy's abilities or popularity. This rival could be the one who instigates the events that lead to Percy's disownment. And then there might be a mentor - like figure outside of the family who takes Percy in after he's disowned and helps him to grow and face his new situation.
Maybe there are some dark forces at work. They sense Percy's growing power and want to stop him before he becomes too strong. These could be ancient evils that have been awakened by Percy's power development. They could send minions or create illusions to make Percy's training difficult.
Obviously, Percy would be one of the main characters. Since it's about him training in Tartarus. And Annabeth might also be involved. Maybe she's helping him in some way, or she's waiting for him outside Tartarus while he trains.
The Underworld could also be a setting. He might be training there to face the dark forces. The dangerous environment full of monsters and traps would provide him with ample challenges to improve his combat and survival skills.
A wise old shaman from an Alaskan tribe might be a supporting character. The shaman could have deep knowledge of the spiritual side of Alaska and guide Percy in his training, perhaps helping him to connect with the forces of nature there.
There could be new characters introduced as well. For example, an old wizard or witch who has knowledge about the specific creature inheritance Harry has. They could be a mentor figure, teaching Harry how to control and use his newfound abilities. And of course, the antagonists like Voldemort would be affected by Harry's new powers. They might try to find a way to counter or steal Harry's creature inheritance powers.
Sasuke could be involved. Since they have a complex relationship, Sasuke might either be a rival during Naruto's training, pushing him to be better, or he could end up joining Naruto in some training sessions to become stronger together.
There could be some minor gods or spirits as supporting characters. For instance, a nymph that lives near Percy's training area could provide him with fresh water or food when he needs it. A small god of the forest could give Percy advice on how to use the natural elements around him for his training. And there could be an old demigod who has retired from battles and now lives near Percy's training place. He shares his old war stories with Percy, which gives Percy new ideas and motivation for his training.