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.
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.
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.
The characters could interact in various ways. Percy could use his ability to understand Ancient Greek to communicate with the cavemen if they have some sort of connection to the old language. For example, if they are descendants of an ancient Greek - influenced civilization. Or, Percy might use his powers to perform feats that the cavemen would see as magic, and they would either revere or fear him based on that.
In these fanfictions, the demigods often try to understand the SCPs from their own perspective of good and evil. They might see some SCPs as new kinds of monsters to defeat. On the other hand, some SCPs could be seen as potential allies if they share a common goal. For instance, if there is an SCP that is being hunted by a more dangerous entity, the demigods could form a temporary alliance with it. The interactions are full of tension and discovery as the two different worlds collide.
Percy would probably be very cautious around Morathi at first. Given his experiences with tricky and powerful beings, he'd be on guard. Morathi, being the conniving character she is, might try to charm Percy or manipulate him. For example, she could use her allure to make Percy lower his defenses, but Percy's loyalty to his friends and his own sense of right and wrong would likely make him resist.
Well, in many fanfictions, their interaction begins with confusion. Since they are from different fictional universes, they have different ways of doing things. However, they quickly realize that they can learn from each other. Percy is impressed by Hermione's vast knowledge of magic theory, while Hermione is in awe of Percy's connection to the gods. They team up to face challenges. In some stories, they have to fight against common enemies that threaten both their worlds. During these battles, their interactions are intense. Percy might save Hermione from a monster, and in return, Hermione would use her magic to heal Percy's wounds. Their relationship grows stronger as they rely on each other more and more.
Annabeth, if she were with Percy, would be more interested in the architecture and strategic planning of Troy. She could offer her knowledge to the Trojans or the Greeks, but they might not trust her either. And Percy would have to protect her from those who might see her as a threat or a sorceress.