Perhaps a story where Percy gets transported to a different era in the demigod world. He could be in the time when the first demigods were discovered and has to deal with the primitive and different rules and threats of that time. He might also learn some long - forgotten secrets about his own powers.
One idea could be that the forgotten demigod discovers a hidden power within themselves that is related to an ancient and forgotten god. This power could set them on a journey to find out more about their heritage and also put them in a position to save the demigod world from a new threat.
Perhaps Percy discovers a hidden prophecy that involves him sacrificing something dear to him to save the demigod world once and for all. This could lead to a lot of internal struggle as he decides what to do. In the fanfiction, he could journey to places never before explored in the original series to find answers.
Another idea is to explore the relationship between the Norse gods and the Greek demigods in a fanfiction. Maybe the Norse gods are intrigued by Percy's powers and want to test him, or perhaps they offer him a quest in the Norse world. This could lead to Percy having to adapt to the different rules and challenges in the Norse realm.
Another idea is that Percy is actually an ordinary human who has been mis - identified as a demigod. He then has to deal with the expectations of those around him who think he has special powers. He might try to prove that he's not a demigod while also getting caught up in the demigod - related events due to his associations. This could lead to some comical and also tense situations as he tries to convince everyone he's just an average guy.
One idea could be that the demigod gun is powered by celestial bronze. It could shoot bolts of energy that can temporarily stun monsters, like a more advanced version of a stun gun. This would give Percy an edge in battles against powerful foes.
One interesting story could be about a Japanese demigod who has a special power related to Japanese mythology, like the ability to control kami. They might team up with Percy Jackson on a quest that involves both Greek and Japanese mythological elements.
One plot idea could be Percy having to team up with Hera to rescue a group of demigods who have been captured by an ancient monster. Hera, despite her usual aloofness, realizes she needs Percy's unique skills.
A really interesting plot could involve Percy being in a situation where he has to use the powers he inherited from Gaea to save the world from a new and greater threat. However, the other demigods don't trust him at first. So he has to not only fight the external threat but also earn the trust of his comrades. He might discover ancient secrets about Gaea that could either doom or save the world, and he has to make a difficult choice based on that knowledge.
One idea could be Percy and his friends getting trapped in a virtual game world that's a twisted version of their own. They have to use their demigod skills to defeat the digital monsters and find a way out.
Maybe Percy is sent on a quest to Atlantis because there are rumors of a traitor among the Atlanteans who plans to side with the Titans. Percy has to navigate the complex political situation in Atlantis and figure out who the traitor is before it's too late. He also has to deal with the Atlantean magic which is different from what he's used to.