One possible plot could be Percy dealing with PTSD from Tartarus while trying to fit into high school life. He might have nightmares that disrupt his school days and struggle to make friends who can understand his past traumas.
Perhaps there's a new villain, a powerful sorcerer who has a vendetta against Percy. The sorcerer discovers that Percy is now at high school and decides to target the school. He uses his magic to create illusions and manipulate the minds of the students and faculty, turning them against Percy. The sorcerer might also be after the secrets Percy learned in Tartarus, thinking it can give him more power.
In some fanfictions, Percy might be more withdrawn. He has seen the horrors of Tartarus and it could make him less trusting of the world around him. He may also have new powers or a deeper understanding of his abilities that he gained from the experiences there.
One challenge could be dealing with the trauma. Tartarus is a terrifying place, and Percy might have nightmares that disrupt his school life. He could also find it hard to relate to his classmates who have no idea what he's been through.
He could be more cautious. The perils of Tartarus might have made him less reckless. For example, he might think twice before getting into a fight or taking risks that he used to take without hesitation.
In some fanfictions, Annabeth and Percy might struggle with PTSD. They could have nightmares about their time in Tartarus. Percy might be overly protective of Annabeth, and they may need time to heal their emotional wounds together.
Perhaps the antagonist could be a corrupted demigod. Someone who was also in Tartarus, but instead of coming out stronger in spirit like Percy, they were twisted by the darkness there. They now want to bring that same darkness to the world of the demigods and see Percy as the main obstacle to their plans.
The main character is Percy, no doubt. However, in this type of fanfiction, we could also expect to see characters like Thalia Grace. She has her own connection to Percy and could offer a different perspective on his situation. The centaur Chiron might also be a main character as he is often a guiding figure for the demigods. And there could be new characters introduced, perhaps other dark - themed characters who are either drawn to Percy or are trying to oppose him because of his changed state.
One possible storyline could be Percy struggling with PTSD after Tartarus. He might have nightmares and be overly cautious in battles. For example, he could hesitate when facing certain monsters that remind him of the terrors in Tartarus. Another could be Percy's changing relationships. Maybe his friends don't fully understand what he went through and he has to deal with feelings of isolation. He could also discover new powers or a deeper connection to his godly heritage as a result of his Tartarus experience.
Perhaps they go on a quest to find a way to close the gates of Tartarus permanently. This would involve traveling to different places, facing new monsters, and using their combined knowledge and skills. Along the way, their bond would be tested, and they'd have to rely on each other more than ever, making their relationship even deeper.