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.
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.
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.
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.
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.
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.
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.
The plot could involve Percy being sent on a quest by Chiron after strange omens related to the Eye of Odin start to appear at Camp Half - Blood. Percy discovers that the Eye has the power to see into the future, but only for those who are worthy. As he searches for it, he is opposed by a group of villains who want to use it to rule the world. Percy must race against time to find the Eye first and decide what to do with its power.
In some fanfictions, Percy as Odin's son could be involved in a power struggle within Asgard. Maybe there are those who don't believe he is worthy of his status, so he has to prove himself not just to them but also to himself. He might have to learn new magic or fighting techniques specific to Asgardian culture to gain respect.
His powers would likely be a blend of his original demigod abilities and those of Odin. He may still retain some connection to water, but it could be transformed. Maybe he can turn water into ice like the Norse frost giants. Also, he could have Odin's gift of knowledge, which means he could understand ancient languages or know things about the past and future without being taught. This would give him an edge in battles and quests compared to the original Percy.