He might introduce new relationships among the gods. Maybe a forbidden love between a god of the sun and a goddess of the night, which would create a lot of drama and conflict. This could lead to power struggles and changes in the divine hierarchy. He could also create new backstories for the gods, like a god who was once a mortal and achieved divinity through an extraordinary act of kindness.
Percy Jackson is likely still one of the main characters. After all, he's the central figure in the original series. And Annabeth might also be there, as she's always been by Percy's side.
Well, one interesting concept could be the new power dynamics. With new gods introduced, it might change how Percy and his friends interact with the divine world. Maybe the new gods have different rules and values compared to the old ones.
Perhaps a fanfiction where the New Gods create a sort of competition for demigods. Percy enters this competition and discovers that there are rules he's not used to, and he has to use his wits and skills in new ways to win. And along the way, he makes some unexpected allies among the new gods.
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.
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.
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.
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.
The new wand might have a core that is a combination of multiple magical elements. For example, a strand of a unicorn's hair combined with a shard of a powerful magical crystal. This would make the wand extremely versatile, able to channel different types of magic depending on how the wizard holds it and the incantation used.