One possible plotline could be Percy accidentally making an earthquake during a battle and then having to deal with the aftermath, like rescuing people. Another could be Percy learning to control his power to create earthquakes as part of his training.
In some fanfictions, Percy's earthquake - making could be a result of his emotional state. Maybe he gets really angry or scared and that triggers an earthquake. Then the story could be about him learning to control his emotions so he can better control his power. Also, it could be that an enemy tries to manipulate Percy into using his earthquake power for their own evil purposes.
One possible plotline could be that an enemy tries to seduce Percy to turn him against his friends. This would create a lot of internal conflict for Percy as he has to fight against the charm or allure of the seducer while staying true to his comrades.
One possible plotline could be that Percy has been kidnapped by some mysterious enemy. Maybe it's a new villain who has a vendetta against him. His friends then start a search mission to find him, facing various challenges along the way.
One possible plotline could be Percy going through some sort of extraordinary adventure that changes Artemis's view of him. Maybe he saves her in a way that no one else could, and this new - found respect and connection gradually turns into love, leading to their marriage.
Another plotline could be that they are babysitting a group of demigod toddlers at Camp Half - Blood. The toddlers keep getting into mischief, like stealing nectar and ambrosia. Percy and Annabeth have to keep them in line, teach them about the rules, and also make sure they don't accidentally harm themselves with their budding powers. It could be a really cute and chaotic story.
One possible plotline could be Loki using Percy for his own mischievous ends. Maybe Loki wants to cause chaos in Percy's world, so he takes control of Percy and makes him do things that disrupt the normal order, like causing trouble at Camp Half - Blood.
Perhaps Medusa has some crucial information that Percy needs to save the world, and in order to get that information, he has to protect her from other threats. So he embarks on a journey to keep her safe.
One possible plotline could be the shock and chaos that ensues within the demigod world when they find out about Hera being pregnant with Percy's child. There would likely be a lot of disbelief and political unrest as Hera is a goddess and Percy is a demigod.
A possible plotline could be Percy being assigned to a top - secret mission by Shield. He has to use his unique skills to infiltrate an enemy organization. Another plotline might be that Percy discovers a conspiracy within Shield itself and has to decide who to trust while trying to expose it.
One possible plotline could be that Percy has been betrayed by his closest friend. Maybe this friend revealed a big secret of Percy's, and now Percy feels isolated and heartbroken. He might start to question his relationships and his place in the world.
One possible plotline could be that Percy has been wronged by Artemis in some way, perhaps she made a decision that put Percy or his friends in danger, and now he's out to punish her by thwarting her plans. For example, if Artemis made a deal with a villain that backfired on Percy's team, Percy might seek revenge.