She could be a creation of a powerful witch who has a vendetta against the demigods. The witch uses dark magic to create the succubus and sends her to the Percy Jackson world. The succubus then uses her charm and powers to get close to Percy, either to steal his powers or to use him to get to the other demigods at Camp Half - Blood.
Blue food could be used as a form of currency in the underwater parts of the Percy Jackson universe. For example, blue sea - grapes could be like gold coins for the mer - people. Percy has to learn about this new form of currency when he dives deep into the ocean on a mission.
Maybe one of the primordial deities, like Gaea, could be the main character. The fanfic could explore her thoughts and actions as she was one of the first beings. It could show how her relationship with other primordial deities influenced the future of the universe, and how her actions in the beginning set the path for events that would unfold much later in the Percy Jackson series.
In many fanfics, Lucifer's presence can create moral dilemmas for the characters. Percy, who is used to a world of somewhat clear - cut good and evil (in terms of Greek mythology), now has to deal with Lucifer's more nuanced nature. This can lead to interesting internal struggles for Percy as he decides whether to trust or oppose Lucifer.
Well, perhaps the succubus is sent by an enemy of the gods to disrupt Percy's relationships with his friends. She starts causing jealousy and strife among them by using her alluring powers. Or maybe she's tied to an ancient prophecy that Percy is involved in, and he has to either defeat her or convert her to the side of good to fulfill the prophecy.
A succubus can be incorporated as a trainer. She could use her charm and allure to her advantage during battles, perhaps distracting opponents. For example, she might have a unique battle style that involves a bit of seduction.
The morale among the demigods would be greatly affected. The Hunt is often seen as a symbol of strength and unity for female demigods. If Percy kills them, it might create a divide between male and female demigods, leading to internal conflicts within the demigod community. Also, it would change the way demigods view Percy. Some might see him as a hero for eliminating a potential threat, while others would see him as a murderer for killing the Hunt.
In some Percy Jackson fanfictions, Excalibur might be incorporated as a powerful weapon that finds its way into the hands of a demigod. It could be a plot device to add more power and mystery to the story.
A succubus familiar can be incorporated by first establishing its magical nature. For example, it could have powers related to charm and allure, which are common traits of succubi. In a fanfiction, it might be a familiar that a dark wizard or an outcast wizard has. The succubus familiar could use its charm to help its master in various ways, like getting information from other characters or sneaking into restricted areas.
A possible plot could involve a character going back in time to the beginning of the universe. This character, perhaps a demigod with special powers, witnesses the formation of the cosmos. They see how the different elements of the Percy Jackson world, like the Underworld, Mount Olympus, and the various magical creatures, came into existence. It could also explore how the concept of demigods was first conceived during these early times.
One way could be by making him a mysterious new demigod. He could have his Sharingan ability which might be related to some special power in the Percy Jackson universe, like being able to see through the Mist more clearly than others.