Maybe it's a group within the Ministry of Magic who oppose Harry's influence on Teddy. They might see Harry as trying to groom Teddy to be his successor in some way and want to stop them from leaving together to prevent this.
It could be an ancient dark wizard who was trapped in a time - locked state but is now released due to the time - traveling disruptions caused by Harry and Teddy. This wizard might see them as threats to his own dark designs on the wizarding world and try to eliminate them.
It could be a dark wizard from the past who senses Teddy's anachronistic presence and tries to use his time - traveling knowledge for evil. Maybe a wizard who was on the verge of creating a really dark magic but was stopped in the original timeline, and now with Teddy's interference, he gets a second chance.
Maybe Voldemort. If the fanfiction combines the Twilight and Harry Potter universes, Voldemort might see Edward as a threat because he is a vampire and could be allied with Harry. So he tries to drive a wedge between them and make Edward leave Harry.
Voldemort could still be the main antagonist. Even if Harry leaves his parents early, Voldemort might be hunting for him due to the prophecy. His dark presence would be a constant threat, driving Harry's actions and the plot of the fanfiction.
It could be a new villain who specifically targets Beast Boy because of his connection to the Titans. This villain might want to use Beast Boy as a way to get to the Titans or to prove his own power. For example, a powerful sorcerer who wants to steal Beast Boy's shape - shifting abilities for his own dark magic.
Voldemort's remaining followers could be the antagonists. Even though Voldemort is gone, there are still some Death Eaters who are bitter about their loss. They might see Harry leaving with Fleur as an opportunity to get revenge on Harry or to use Fleur as a hostage to gain power. They could try to ambush them on their journey, creating a lot of dangerous situations for Harry and Fleur.
It could be a new dark wizard who is secretly operating within Hogwarts. He might be trying to steal powerful magical artifacts and Harry and Luna get in his way.
There could be a group of magical creatures who see the snake as an abomination or a threat to their kind. They would try to destroy the snake and Harry would have to protect it. These creatures could be from a part of the Forbidden Forest that has not been explored much in the original books and they have their own set of rules and magic which makes them a formidable antagonist.
The Ministry of Magic could be the main antagonist. They might be the ones who spread lies or misinformation about Harry, causing everyone to abandon him. They could be afraid of Harry's power or have some ulterior motives to get rid of him. They could use their influence and authority to turn the public against Harry, making his life a living hell as he tries to survive on his own.
Surprisingly, it could be Bellatrix herself. Despite being enslaved, her mind could be so twisted that she constantly tries to break free from Harry's control and undermine his actions. She might try to secretly communicate with Voldemort or other Death Eaters, making her an internal and dangerous antagonist for Harry.