Well, in such a fanfic, perhaps Percy ends up in a new camp or place full of demigods he doesn't know. He has to prove himself without his mom's support. He could befriend some unlikely characters who help him understand more about his mother's disappearance. And in the end, he might find that his mom left to protect him from a greater threat that he now has to face on his own.
It could be a new powerful monster that was sent after Percy because his mom was no longer there to protect him. Maybe a monster that has a grudge against Percy's family.
One possible plot could be Percy feeling a deep sense of betrayal and loneliness. He might struggle with his self - worth as he wonders why his sister left him. This could lead him on a journey to find answers about his family and his own identity, perhaps even uncovering secrets about his demigod heritage that his sister knew and he didn't.
One possibility is that Percy sacrifices himself to save his friends and Camp Half - Blood from a powerful, unbeatable enemy like an ancient primordial god. He might use his powers to create a shield or diversion that allows everyone else to escape while he faces certain death.
One possible plot could be that Percy wakes up in the mental hospital with no memory of how he got there. He starts to notice strange things like the nurses and doctors seem to have an otherworldly aura. As he tries to regain his memory, he discovers that the hospital is a front for some sort of mythological experiment. He then teams up with other demigods who are also trapped there to escape and expose the truth.
One possible plot could be that Percy is overwhelmed by the pressure of his demigod duties. He has constantly faced life - threatening situations, seen friends die, and felt the weight of the prophecy on his shoulders. In this fanfic, he might see shooting himself as a way to end the cycle of pain and danger for himself and those he loves.
The plot could involve Percy being abandoned by camp because the camp leaders fear his growing power. He wanders the world, feeling lost and angry. Percy then encounters a mysterious figure who offers him a way to get revenge on the camp. However, Percy, being a hero at heart, realizes that taking revenge won't solve anything. Instead, he decides to find evidence to clear his name and expose the real danger that the camp is ignoring while he was being pushed away.
Maybe the sister had some dark secrets that she was afraid Percy would find out. For example, she could be involved in something illegal or dangerous, and to protect Percy from getting dragged into it, she chose to abandon him.
One possible plot could be Percy going on a solo quest specifically designed to help him master his powers. He might face challenges that force him to use his water - based powers in new and extreme ways, like having to freeze an entire lake to stop a monster from escaping. Along the way, he could meet a new mentor, perhaps an ancient water spirit, who teaches him secrets about his abilities that he never knew before.
A possible plot could be that Kratos is somehow transported to Percy's world. Percy initially mistakes Kratos for a new threat but then realizes they could work together. They join forces to stop a dark god from rising who wants to destroy both their worlds.
One possible plot could be that Percy is found by a kind-hearted hermit who lives in the woods. The hermit raises Percy in seclusion, teaching him basic survival skills and a unique form of magic unknown to the outside world. As Percy grows, he starts to have strange dreams about his past and his real parents. Eventually, he decides to leave the safety of the woods to search for his true identity.