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.
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.
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 he wants to change the system. Percy has always been a bit of a rebel, and in fanfiction, he could see the gods' rule as corrupt or unfair. So, killing them could be his way of starting anew and creating a better world for demigods and mortals alike. Another motive could be to prevent a greater evil. If he discovers that the gods are planning something that would destroy the world, he might decide that killing them is the only way to stop it.
In this kind of fanfiction, it might be related to the idea that Percy has a connection to a primordial force. This force could have been around before the gods came into being. For example, if Percy has a link to the very essence of the universe that was there before the gods were created, it could make him seem older in a very fundamental way. This could also tie into his powers, like his control over water. If water is seen as a more ancient element than the gods themselves in the context of the story, his power over it could contribute to this idea of being older.
Well, it could start with Percy being framed for a crime he didn't commit by the gods. This false accusation makes him feel extremely betrayed. He then has to go on the run while trying to prove his innocence. Along the way, he meets other outcasts and together they form a resistance against the gods. They might try to find a way to hold the gods accountable for their actions and create a new order where demigods are treated more fairly.
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.
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.
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.
One possible plot could be that the entire Greek pantheon is thrown into chaos. Percy might be seen as a huge threat, and other gods and goddesses would either try to hunt him down or form alliances with him out of fear or a desire for power. Demigods would be forced to take sides, leading to massive battles among them.