There might be some new characters introduced in the fanfiction who have different ideals or motives that clash with Annabeth's. These new characters could be the antagonists as they oppose Annabeth, and Percy has to step in. For example, if they think Annabeth's way of handling a certain quest is wrong and Percy believes in her, he'll fight against their ideas.
Perhaps in the fanfiction, there are other characters who are jealous of Annabeth's intelligence or skills. So they start spreading rumors or making unfair remarks. Percy defends her because he knows her true worth and capabilities. He would stand up and say things like 'You don't know her like I do. She's always been there for all of us.'
It could be an old enemy from Greek mythology that has been resurrected. For example, a powerful Titan who has a vendetta against the demigods, especially Percy and Annabeth.
It could be the traditional villains from the original story, like the Titans or some powerful monsters. They might torture Percy to get information or just to cause chaos.
Often, it could be old enemies like the Titans. In fanfiction, they might return in new and more devious ways. For example, Kronos could have a new plan to break Percy and Annabeth apart before trying to take over the world again.
Even old enemies of the demigod world, who see Percy and Jason as threats, could be the antagonists. They might use deception and betrayal as a way to weaken the demigod forces, knowing that Percy and Jason are important figures among them.
It could be the traditional villains from the original story. Maybe some of the old enemies of Percy who have a vendetta against him. For example, the Titans or some rogue demigods who oppose him for power or personal reasons.
The gorgons could be a likely villain. They might be lurking in the catacombs of Paris, waiting to turn Percy and Annabeth into stone. They could be after some powerful magic item that is hidden in the city.
Aphrodite could also be one of the spying gods. Since she loves meddling in love affairs, and Percy and Annabeth's relationship is quite famous among the demigods. She might be spying to see how their relationship develops and perhaps add a little nudge here and there if she feels like it.
Often, it could be a jealous classmate. Maybe someone who has a crush on Percy and sees Annabeth as a threat, so they try to create problems between them. Another could be a strict teacher who doesn't like Percy's carefree attitude and Annabeth's independent thinking, always trying to give them a hard time.
The old enemies of Percy and Annabeth like the Titans or some of the more vengeful monsters could be the main antagonists. They might see the unborn child as a threat or an opportunity to get back at Percy and Annabeth.