A new villain could be introduced, perhaps a demigod gone bad who is jealous of the special baby. This villain might see the baby as a threat to their own plans of power in the demigod world and tries to stop it from growing up.
It could be an old enemy from their past, like a vengeful monster. Maybe a cyclops that they once defeated and now it wants to take revenge on them through their baby.
Well, one possibility could be that the baby has some sort of special power. Maybe it can communicate with the gods in a unique way. Since Piper has her charm - speaking abilities and Annabeth is super smart, the baby might inherit a combination of these traits and use them to solve problems in the demigod world.
A group of rogue demigods could be the main antagonists. They might be jealous of the attention the daughter gets because of her parents. So, they plot to make her life difficult and try to drive a wedge between her and the other demigods.
The main antagonist might be an ancient and powerful being that has awakened. This being could see Percy and Annabeth as a potential threat to its plans of taking over the demigod world. So, it uses its influence to have them banished, thinking that without them, it would be easier to conquer. For example, a long - forgotten Titan who has found a way to break free from its prison.
It could be an ancient and powerful being from the chaos realm who sees Percy and Piper as intruders and a threat to its own power. This being might have been ruling over a certain part of Chaos for eons and doesn't want the demigods to disrupt the status quo.
Another vampire family that is jealous of the Mikaelson's power and influence. They see the baby as a threat to their future plans. They might try to kidnap the baby and use it as a bargaining chip to gain more power in the vampire world. They would be constantly plotting against the Mikaelsons to get their hands on the baby.
Danzo could be a great antagonist even when Naruto is a baby. He might see Naruto as a threat to his plans for Konoha's future and try to get rid of him secretly while making it look like an accident.
Ares could also be a strong antagonist. He might view the alliance between Annabeth and Zeus as a threat to his own plans for power and chaos. He could try to start wars or create discord to break their alliance and stop whatever they are working towards.
It could be an old enemy of Percy and Annabeth. Maybe a monster that they thought they had defeated long ago but has come back for revenge. This time, it might target Annabeth's daughter to get back at them.
A powerful dark wizard could be a great antagonist. He might want to use the Scarlet Baby's unique energy for his dark magic. He could send his minions, like flying monkeys or shadow serpents, to capture the baby.
A human noble who doesn't approve of Ariel and Eric's union and especially doesn't like the idea of a half - human, half - mermaid baby. This noble could try to create problems for the family, like spreading false rumors or trying to get the baby separated from its parents. Another possibility is a sea monster that has been awakened by the birth of the baby, seeing it as an intrusion in its territory and trying to harm the baby and its parents.