In some cases, it might not just be the gods in their true forms. There could be demigods who are loyal to the gods and believe that Percy is wrong for running. These demigods could be manipulated by the gods into thinking that Percy is a threat to their world. So, they would also act as antagonists, trying to stop Percy from achieving his goals and turning him over to the gods.
It could be some of the more vengeful gods, like Ares. If Percy has somehow angered him in the past, Ares would be more than happy to hunt him down. Also, the gods' enforcers, such as the minor deities who do their bidding, could be antagonists too. They would be the ones doing the legwork to find Percy while the major gods give orders from Olympus.
The traditional gods who don't want to see Percy as king could be antagonists. For example, Zeus might see Percy as a threat to his power and try to stop him at every turn.
Well, it could be that Percy has had enough of the gods' constant interference in his life. He's always been their pawn in some way, and now he decides to run. He might go into hiding in the mortal world, using his skills to blend in. Along the way, he could meet other demigods who also feel the same way about the gods and together they form a sort of resistance, trying to make the gods see how their actions are affecting the demigods.
Other jealous demigods could act as antagonists. They might feel that Percy doesn't deserve the blessings and try to undermine him. They could spread rumors or even try to sabotage his quests to make him look bad in the eyes of the gods.
The main antagonists would most likely be the gods themselves. Since the title mentions being hunted by the gods, they would be the ones sending various threats Percy's way. It could be Zeus, who is often quick to anger and punish those he thinks are a threat to his power.
It could also be that the Olympian Council as a whole acts as the antagonist. They might have made decisions that Percy sees as a betrayal, such as sacrificing the safety of demigods for their own political gain. Each god on the council, with their own self - interests, might contribute to Percy's feeling of betrayal, making the council as a whole the main force he has to oppose.
Obviously, the gods themselves would be the main antagonists. They have the power to manipulate Naruto's world and his fate. They could be some sort of ancient deities who have been watching over the ninja world from afar and now feel the need to interfere.
The Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
The main antagonists in a 'Percy back in time fanfic' could be the followers of the Titans. They were numerous and loyal to Kronos. They would view Percy as an enemy since he is from a time when the Olympians are in power. Additionally, if Percy travels to a time when a powerful and evil demigod once lived, that demigod could be an antagonist. For example, if he goes back to a time when a demigod was on a path of destruction before being stopped, Percy's arrival might disrupt the events that were supposed to stop that demigod, and so the demigod would turn against Percy. There's also the possibility of some ancient sea monsters that were more prevalent in the past and were under the control of the Titans or other evil forces.
The Titans could still be antagonists. Since Percy has a connection to Hecate, they might see him as a threat to their plans of overthrowing the gods. They could try to capture him to use his powers for their own evil purposes.
There could be his best friend Grover. Grover might try to find Percy after he runs away, adding an element of search and rescue to the story.