One possible plot could be Percy sacrificing himself to save his friends while in Poseidon's arms. Maybe there's a great battle against an unbeatable foe, and Percy realizes the only way to victory is through his own death. He accepts his fate in Poseidon's comforting embrace.
Perhaps in the fanfiction, Percy has been poisoned or cursed in a way that can't be undone. He goes to Poseidon for solace in his final moments. Poseidon, being his father, holds him as he passes away. And this event could trigger a series of reactions among the other characters, like Annabeth vowing revenge or the demigods uniting in a new way to honor Percy.
It could be an ancient and powerful Titan that has risen again. This Titan might have a vendetta against Poseidon and targets Percy as a way to hurt him. Since Percy is Poseidon's son, his death in Poseidon's arms would be a great blow to the sea god.
One possible plot could be Poseidon's grief and his journey to seek revenge for Percy's death. He might use his power to disrupt the world that allowed such a thing to happen. Another could be Poseidon trying to bring Percy back to life, going against the rules of the gods and facing many challenges along the way. Or perhaps Poseidon watches as the world changes after Percy's death, seeing how the other demigods step up or fall apart without Percy's leadership.
One interesting plot could be Percy having to prove himself to Poseidon in a new and unexpected way. For example, he might have to solve a mystery that is directly related to Poseidon's power over the sea but in a realm that is unfamiliar to both of them, like an underwater civilization that has been lost for centuries.
Maybe in the fanfic, Percy's death could be a sacrifice to save Zoe. This would then lead Zoe to live her life in a way that honors Percy's sacrifice. She could become a protector of the things Percy held dear, like a certain place or group of people. And as she does this, she has flashbacks of their time together, which are bittersweet memories that keep her going.
Perhaps it's part of a grand plan that Poseidon has, one that he believes will ultimately benefit Percy but in the short - term causes him pain. For example, he might be trying to toughen Percy up or make him prove himself in a more extreme way, thinking it will help Percy in the long run.
One possible theme could be family reconciliation. Since Percy and Poseidon have had a somewhat rocky relationship at times, a cuddle scene could symbolize them mending their differences and growing closer as father and son.
A great plot might be that Poseidon has to protect baby Percy from other mythological beings who sense his potential power. So he hides Percy in a special place where only he can find him. This could lead to all kinds of adventures as Poseidon has to fend off threats while keeping Percy's existence a secret.
Another plot could involve time - travel gone wrong. Marinette tries to go back in time to fix a major mistake, but something disrupts the time - space continuum and she gets caught in a loop that ultimately leads to her death.
Many fanfictions center around Poseidon's role in prophecies. In the Percy Jackson world, prophecies are a big deal. So, in these stories, Poseidon could be trying to manipulate or fulfill prophecies that involve Percy. He might be working with or against other gods to ensure a certain outcome. There are also plots where Poseidon discovers new secrets about Percy's destiny and has to take action to either protect or guide him in a way that wasn't in the original narrative.
One possible plot could be Poseidon teaching Percy about his underwater powers in a really fun and father - son way. For example, they could have little adventures in the ocean where Poseidon shows Percy how to communicate with sea creatures. Another plot might involve Poseidon protecting Percy from the other gods who are jealous of Poseidon's special relationship with his son. Maybe he creates a hidden underwater lair for Percy to grow up safely.