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.
In this fanfiction, Poseidon is a key god with possessive traits towards Percy. Since Percy is his son, he has a natural inclination to be possessive. Another god could be Athena. She might see Percy's potential and want to have some sort of control over him for the sake of knowledge or strategic reasons.
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.
Probably Poseidon, as he is Percy's father and has a vested interest in his son's well - being. Zeus might also be protective in some cases, despite their past differences, as Percy is a hero who often saves the world which benefits Zeus's realm as well.
In the fanfiction, Percy's possessiveness might also be demonstrated by his need to be included in all of Annabeth's plans. He may feel left out or threatened if she starts making plans with other people without him. He wants to be a part of everything she does, almost like he owns a part of her time and attention.
Well, without reading the specific fanfiction, it's hard to say exactly who Percy is. But generally, in a 'champion of the gods' scenario, Percy would be a central figure. He might be a hero with unique powers, like being able to control certain elements or having superhuman strength. He could be a character who has to face various challenges and tasks on behalf of the gods, kind of like a chosen one in a fantasy story.
Aphrodite could also be one of the spying gods. Since she loves meddling in love affairs, and Percy and Annabeth's relationship is quite famous among the demigods. She might be spying to see how their relationship develops and perhaps add a little nudge here and there if she feels like it.
Poseidon would probably be one of the main gods watching. Since Percy is his son, he would have a strong interest in his well - being during the fight.
The gods might show their protection in various ways. For example, they could directly intervene in battles Percy is in, using their divine powers to shield him from harm. They might also send him signs or omens to guide him away from danger.
Zeus is a possibility. As the king of the gods, he might see Percy's potential and adopt him to have an ally among the demigods. Another could be Poseidon, since Percy is already his son in the original story. It would be an interesting twist to have Poseidon formally adopt Percy in a more divine way.
One way is through their actions. For instance, the Hunt might always be by Percy's side, not giving him much personal space. They could be very quick to defend Percy from any perceived threat, even if Percy doesn't think it's necessary.
Hestia's possessiveness can shape the plot in many ways. It might lead to Percy being isolated from other characters who could be important to his development. This in turn can create a series of events where Percy has to either break free or come to terms with Hestia's possessive nature. Also, it could attract the attention of other powerful beings who either oppose or support Hestia's possessiveness, adding more twists to the plot.