It could be Hades. He might not like the idea of Percy, a son of Poseidon, being friends with Apollo. Hades could see it as a threat to his own power or plans in the underworld.
A new villain could be created for this fanfiction. Maybe a powerful sorcerer who discovers their secret friendship and tries to use it against them. This sorcerer could be after the power that Apollo and Percy possess together and wants to break their friendship to gain that power for himself.
It could be an old enemy of the gods, like Kronos. Even though he was defeated before, he could find a way to come back and target Percy and Apollo specifically. Since Percy has been a thorn in the side of many of the Titans' plans before, and Apollo is a powerful god, Kronos might see them as a threat to his new - found or potential power.
Perhaps the plot involves Percy helping Apollo with a secret mission. Since Percy is good at handling tough situations, he could be assisting Apollo in retrieving a lost artifact. They keep their friendship a secret because Apollo doesn't want the other gods to think he's relying too much on a demigod.
It could be a dark figure from Greek mythology who wants to stop Naruto from fulfilling Apollo's will. Maybe a Titan who is jealous of Naruto's new - found connection to Apollo.
A powerful new demigod who is jealous of Percy's secret power could be the main antagonist. This demigod might think that Percy doesn't deserve such a power and tries to steal it for himself. He could be a son or daughter of a minor god who feels overlooked and wants to use Percy's power to gain recognition.
Well, it could be about Percy and Apollo becoming friends in an unexpected way. Like, Apollo is in a situation where he loses his godly powers temporarily and Percy helps him out. During this time, they bond over their shared experiences of being different from regular humans. They start to understand each other's strengths and weaknesses, and form a strong friendship.
It could be a jealous student. Maybe there's a Gryffindor who is envious of Creevey's friendship with Harry. This student might spread rumors about Creevey, saying that he's only using Harry for his fame. This causes some tension between Harry and Creevey at first, but they eventually figure out the truth and strengthen their bond in the face of this false accusation.
It could be a new character, like a powerful wizard who has a grudge against Percy for some reason. Maybe Percy accidentally disrupted one of his spells, and the wizard is out to get him, which makes Percy mad.
Perhaps a jealous sea nymph. She has always been envious of Amphitrite's position and power. When she sees Amphitrite bonding with Percy, she decides to be the antagonist. She spreads false rumors about Percy among the sea creatures, causing some to be wary of him and Amphitrite's association with him. She might also try to sabotage any attempts at further bonding between them, like ruining a special ceremony or event they were planning to attend together.
It could be a new god or goddess who is jealous of the attention Percy gets. Maybe they try to disrupt the conversation between Athena and Percy to cause chaos.
It could be the warden of the prison. The warden might be a cruel and power - hungry person who wants to keep Percy imprisoned for his own reasons, like getting some sort of reward or power from those who put Percy there.