Zeus is often one of the main gods showing possessiveness. He sees Percy as a powerful asset or a potential threat, so he wants to keep Percy in check. Poseidon, as Percy's father, also shows possessiveness in a different way. He wants to protect Percy but also use his powers for his own purposes sometimes.
Well, it could affect the plot in various ways. The gods' possessiveness might mean that Percy has limited freedom. He may constantly be under the watchful eyes of the gods, which restricts his actions. Also, it could lead to power struggles among the gods themselves, with Percy caught in the middle. Maybe one god tries to protect Percy from the others' possessive actions, adding more twists to the story.
In fanfiction, the concept of Ares being possessive of Percy can also stem from the idea of forbidden or complex relationships. The contrast between Percy's more heroic and noble nature and Ares' war - like and often brutish ways creates an interesting dynamic. Ares may view Percy as a symbol of what he can't be, and his possessiveness could be a way of trying to corrupt or change Percy to fit his own view of the world.
It could also be due to a sense of ownership. Percy has achieved a lot with the help of the gods, and Athena might feel that she has some claim over him because of the assistance she or other gods associated with her have provided. In the context of the fanfiction, this sense of ownership could translate into possessiveness.
Well, in some fanfictions, Hermes might be possessive of Percy because Percy could possess certain qualities or powers that Hermes wants to control or have an influence over. Maybe Percy has a unique connection to the world of the gods that Hermes sees as valuable.
Well, in some fanfictions, Luke might be possessive of Percy because he sees Percy as a symbol of power or potential. He may want to control Percy to use his abilities for his own goals, like in the original story where Luke has his own dark motives. Also, it could be out of envy. Percy has things that Luke might feel he lacks, so his possessiveness could be a way to try and take what Percy has for himself.
It could be because of the potential for a romantic relationship in fanfiction. Some fans like to explore the idea of Nico having romantic feelings for Percy. In that case, possessiveness might be a natural part of showing his intense emotions. He wants Percy all to himself, not sharing him with others, especially when there are other characters who might also be interested in Percy.
It could be that Aphrodite senses some unique potential in Percy when it comes to love. Maybe she foresees that he will play a crucial role in some grand love - related event in the future. So, to ensure that things go according to her plans, she becomes possessive. She doesn't want other forces or characters to sway Percy from the path she has in mind for him.
It could be that Zoe has a special connection with Percy that she doesn't want anyone to interfere with. So she becomes possessive to safeguard that connection.
Percy could also become angry. He values his freedom and his relationships with his friends and family. Hades' possessiveness is a threat to all of that. So he might stand up to Hades, even if it's a risky move. He'll tell Hades that he won't be controlled or owned. He'll fight back using his powers and his wits. He might also seek help from other gods or his demigod friends who have had experiences with Hades.