The gods also interact with Percy a lot. Zeus might be angry with Percy for interfering in the affairs of the gods in Ancient Greece. Or Poseidon could be guiding Percy secretly, giving him hints on how to deal with the challenges he faces, like when he's on a quest related to the sea.
One great 'Percy Jackson Ancient Greece Fanfiction' is 'The Lost Hero's Quest in Ancient Greece'. It has an exciting plot where the characters are plunged into a forgotten part of Ancient Greek mythology. The author does a wonderful job of weaving in the familiar elements from the Percy Jackson series with new and unique twists from Ancient Greek lore.
In many fanfictions, Percy is likely to meet ancient Greek heroes such as Heracles. They could engage in some friendly competitions or Heracles could offer his strength to help Percy in a difficult situation. Another character he might come across is Pandora. She could be either a help or a hindrance depending on the plot of the fanfiction as she is associated with the box that contained all the evils of the world.
First, do your research on Ancient Greek mythology. Know the gods, the monsters, and the heroes well. For example, if you're writing about Percy facing the Minotaur, you need to know all the details about it from the original myths. Second, stay true to the characters of the Percy Jackson series. Percy is brave but also has a sense of humor, so keep that in his character. Third, create an engaging plot. Maybe it could be about Percy finding a lost temple in Ancient Greece that holds a powerful secret.
One interesting adventure could be Percy exploring the lost city of Atlantis in Ancient Greece. He might face sea monsters and ancient traps while trying to uncover the secrets of the city.
He would probably be cautious at first. Percy knows the power of the gods from his own experiences, but in ancient Greece, they are even more directly in control. He might try to avoid angering them, but if they wronged a mortal unjustly, he would likely speak up. For example, if Zeus was about to strike down an innocent villager, Percy might use his quick thinking to persuade Zeus otherwise.
Percy is, of course, the main focus. However, in many of these fanfictions, Luke Castellan can also be a major character. Since Luke had his own issues with the gods and turned to the dark side in the original series, he could either be an influence on Percy's dark turn or an ally in his new dark journey. Nico di Angelo is another character who could be involved. Given his connection to the Underworld and his own complex relationship with Percy, he might try to understand what's going on with Percy or try to fight against him if he thinks Percy has gone too far.
Annabeth is often the one to save Percy. She's smart and resourceful. For example, she might use her knowledge of architecture to find a way out of a collapsing building that Percy is trapped in. Or she could use her strategic thinking to outwit a monster that has Percy at its mercy.
Well, Annabeth would definitely be one. She's always been by Percy's side, and in this fanfiction, she might be a bit worried about Percy being the champion of Nyx. She could be trying to help him while also being cautious of Nyx's motives.
Draco Malfoy would be a likely character. Given his Slytherin status, he would likely have a complex relationship with Percy. He might start off as hostile, seeing Percy as an outsider, but then they could end up having to work together for some reason.
He would surely interact with Annabeth. Their relationship is central in the Percy Jackson series, so in a Tartarus fanfic, she'd likely be there to support him or be in a similar situation as him.