Another possibility is that Percy is trying to protect someone else. He may have found out that the gods are after a particular demigod, maybe a younger or more vulnerable one. So, he takes it upon himself to hide this demigod from the gods. In the process, he has to hide himself as well to avoid leading the gods to their target.
It could be that Percy has somehow angered a powerful god. Perhaps he accidentally disrupted an important ritual or stole a powerful artifact that belongs to a god. Fearing the god's wrath, he goes into hiding. He might seek refuge in some forgotten corners of the demigod world, like an old, abandoned camp or a hidden cave.
Maybe Percy hides because he discovers a secret about the gods that they don't want him to know. For example, he might find out about some underhanded deal among the gods that could endanger the demigods. So, in order to protect himself and his friends, he decides to hide.
His friends from Camp Half - Blood could be helping him. Annabeth, with her intelligence, might be devising plans to keep Percy hidden and safe. Grover could use his skills as a satyr to find safe hiding places and gather resources for Percy.
Maybe Percy unknowingly breaks some ancient and very strict laws of the Gods. For example, he might interfere with some sacred rituals or places that are off - limits to mortals, even demigods like him. In the fanfiction world, the Gods could be very unforgiving when it comes to such violations and decide to kill him as a result.
In this fanfiction, the plot might revolve around Percy's struggle as a slave of the gods. He could be used as a tool by the gods in their power games. For example, the gods might send him to retrieve powerful artifacts from dangerous places, and all the while he is trying to resist this unjust treatment and regain his freedom.
In this fanfiction, it could be that there is a prophecy that Percy is fated to either save or destroy the gods. Circumstances push him towards the latter. He might learn some dark secrets about the gods' origin that make him believe they are a threat to all existence. So he embarks on a journey filled with challenges and battles to take them down.
One possible plot could be that Percy has somehow angered the gods, perhaps by accidentally disrupting a major ceremony. As a result, they send various mythical creatures to hunt him down. He has to use his wits and demigod powers to outsmart them and find a way to make amends with the gods.
One possible plot could be Percy's struggle to survive in a new, unknown realm after being banished. He might have to find new allies and face new enemies.
One possible plot could be Percy struggling to control new, strange powers that come with the curse. Maybe he has to constantly battle against the dark impulses the curse brings out in him.
Perhaps the fanfiction could center around Percy discovering a hidden prophecy that is the key to ending the war between the gods. He then has to go on a dangerous quest to fulfill it. Along the way, he meets new allies and enemies, and has to use his wits and powers to overcome various obstacles. This could also lead to some character development for Percy as he faces difficult decisions and moral dilemmas.
One possible plot could be that Percy and his friends are faced with a new and extremely powerful threat that endangers not only the mortal world but also the entire pantheon. In order to defeat it, they are offered a chance to become gods. They have to go through a series of trials that test their loyalty, courage, and wisdom even more than before. Percy might struggle with the idea of leaving his mortal life and family behind, but realizes it's for the greater good. Along the way, they face old enemies who are jealous of their potential ascension and try to stop them at all costs.
Perhaps he has lost too many people close to him. If his friends, like Annabeth or Grover, were to die in a particularly tragic way, he could be so grief - stricken that he no longer wants to live in a world without them. He might think that death is the only way to escape the pain of their loss.