Percy would likely be very confused at first. He'd probably feel a mix of anger and sadness. He might start to question his own actions and wonder if he did something wrong to make his sister leave.
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.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
One possibility is that the sister has some unique powers that the Olympians fear. So they abandon her. In the fanfiction, she could be on a journey to discover her true self and her powers, while Percy unknowingly gets involved in her quest. Maybe she's being hunted by some mythical creatures because of her heritage, and Percy has to save her in the end.
It could be a vengeful god. Maybe a god who feels that the sister's existence is an insult to their power. So they set out to stop Percy from finding her. For example, Hades might be the antagonist if he believes that the sister's return could disrupt the order in the Underworld.
One possible reason could be jealousy. Maybe his sister is jealous of Percy's special abilities or the attention he gets. Another reason might be that she is forced to abandon him due to some external threat or danger that she believes will harm her if she stays with Percy. Or perhaps she has been brainwashed into thinking that Percy is a bad influence or a danger to her.
Percy might be initially very confused and hurt. He may try to find his sister and understand why she has left him. He could also become very angry and feel betrayed, which might lead him to take some rash actions.
The sister could be under the control of a powerful god or goddess who has a grudge against Percy. She might be forced to betray him. For instance, she could lead Percy into a trap set by the god. She could lie to him about a mission, saying it's a rescue mission but in fact it's a trap where the god is waiting to take revenge on Percy for some past deeds. This would be a really heart - breaking betrayal for Percy as he trusts his sister.
One way is through facing challenges together. For example, when they are on a quest, they might have to rely on each other's skills. Percy's sword - fighting skills and his sister's magic (if she has any) can complement each other. They also learn about each other's weaknesses and how to protect one another. In addition, they can have heart - to - heart conversations during quiet moments in their adventures, which will deepen their relationship.
One idea could be Percy feeling betrayed by Poseidon and then finding a new family among other outcasts in the demigod world. He could form a group with them and go on adventures that are not related to Poseidon at all.