In this fanfiction, there might be some werewolves who view the baby as an abomination since it's part vampire. They could try to harm the baby, which would put Bella and Stefan in a difficult position to defend their child.
The Volturi could be antagonists. In the Twilight universe, they are the powerful vampire coven that enforces vampire laws. They might see the baby as a threat to their power or a violation of their rules. They could try to eliminate the baby or control Bella, Edward, and their family.
It could be some of the traditional antagonists from the original story, like the Volturi. They might see the baby as a threat to their power or the order they've established in the vampire world.
The Volturi could be antagonists. Since they are the vampire authority, they might see the baby as a threat to the vampire world order. They could be worried about the baby's mixed heritage and its potential power, so they might try to eliminate the baby and even Bella and Klaus. Another possible antagonist could be some of Klaus's old enemies. They might see the baby as a way to get revenge on Klaus, either by kidnapping the baby or causing harm to it and its parents.
One possibility is that the baby has some special powers. In the fanfiction, this could lead to a whole new set of adventures. Bella and Stefan could be on a journey to understand and control these powers while also dealing with their own relationship and the new family dynamic.
Another possibility is that there is a mysterious figure who has some sort of vendetta against the family. This figure could be causing strange and unexplained events to occur around the baby, like making the baby sick in a way that doctors can't figure out at first. This would then be a source of conflict as Bella and Sam try to protect their baby from this unknown threat.
It could be their families if they are against the idea of Bella and Embry having a baby. For example, if Bella's family has high expectations for her and doesn't think Embry is a suitable partner, they could try to interfere and cause problems.
It could be that some of the humans who have discovered the existence of vampires and the new baby become antagonists. They might form a group to hunt down the Cullens and the baby, fearing that the baby could be the start of a new vampire - human hybrid race that could overpower humans.
It could be that an old enemy of Stefan's family decides to target Bella as a way to get back at Stefan. This enemy might be another vampire clan or a supernatural being with a long - standing grudge. They would do everything in their power to disrupt the relationship between Bella and Stefan, causing all sorts of problems and conflicts for the two of them in the fanfiction.
Well, it could be a group of vampires or werewolves who see the baby as a threat to their existence. They might believe that the baby will grow up to be a powerful force against them, so they try to eliminate the baby.
Often, in these fanfictions, other vampires can be the main antagonists. For example, a jealous vampire who wants Stefan for herself might see Bella as a threat and try to drive them apart.