Well, it could be a story full of epic adventures. Percy's demigod powers combined with Odin's influence might lead to him facing new and more powerful foes. He could be trained in different ways than he was in the original Percy Jackson series, learning skills more in line with Norse mythology.
Percy would probably grow in his leadership skills. Odin is often seen as a very strategic and powerful leader in Norse mythology. Under his influence, Percy could learn new ways to lead in battles and make decisions. He might also become more of a diplomat, trying to bridge the gap between the Greek and Norse worlds. For example, he could try to make alliances between Camp Half - Blood and the Norse heroes or gods. This would require him to be more diplomatic and understanding of different cultures.
In most traditional mythologies, Percy Jackson is the son of Poseidon in the 'Percy Jackson' series, and Odin is from Norse mythology. But in fanfiction, anything can be reimagined. So, he could be depicted as the son of Odin in some very creative fan - made stories.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
One plot idea could be Percy having to prove himself to the Norse gods. Since he's the son of Odin in this fanfiction, the other Norse deities might be skeptical. He'd have to go on a quest to show his worth, like retrieving a powerful Norse artifact.
A fanfiction could revolve around the idea that the Eye of Odin has been stolen by a rogue demigod who wants to use its power for his own gain. Percy Jackson is called in to stop this demigod. The Eye of Odin in this story could be a key to unlocking an ancient power that could change the balance between the Greek and Norse worlds. Percy has to learn about Norse magic and lore quickly in order to face this new threat. He might meet some Norse demigods along the way who either help or hinder his progress.
Well, of course, Percy Jackson himself often makes an appearance. He could be a mentor figure to the adopted son, guiding him through the ropes of being a demigod. Annabeth is also common, perhaps helping the adopted son with her wisdom and knowledge of the mythological world.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
Well, in the original Percy Jackson story, Percy is a son of Poseidon. But if he's the son of Odin in fanfiction, his powers would be completely different. Instead of controlling water, he might have powers related to Odin like seeing the future or having a connection with ravens.
One possibility could be that Percy, being the banished son of Odin, has to prove himself in the world of Percy Jackson. Maybe he has powers from Odin that are not fully understood in the demigod world. He could go on a journey to discover his true identity and find a way to regain his place. For example, he might face challenges from both the Norse and Greek mythological beings. He may have to use his wits and newfound powers to overcome these obstacles.