One common plotline is the mystery behind the pregnancy. Is it a result of a forbidden love with another demon or some powerful entity? Writers often use this to create suspense.
Often, the pregnancy is depicted in a way that ties into the overall themes of the Supernatural world. It could be part of a prophecy or some sort of dark magic. Maybe she was cursed with the pregnancy, and it's now a race against time to either get rid of it or use it to her advantage. Fanfic writers might show her dealing with the physical and emotional toll of pregnancy while still trying to maintain her status among demons.
One common theme is power struggle. Abaddon is a powerful demon, so many fanfictions explore her battles for power, either against other demons or the Winchesters. Another theme is her backstory. Writers often delve into her past to give more depth to her character.
One common theme is the struggle between good and evil. Since Abaddon is a demon, her daughter often has to deal with the pull of her demonic heritage while also having the potential for good. For example, in many fanfics, the daughter may be tempted to follow in her mother's footsteps but then has to fight against that urge.
Often, there are plotlines where she teams up with Sam and Dean. They might not trust her at first because she's Bobby's daughter and they're worried about her getting hurt. But then she proves herself to be a capable hunter. There are also stories where she gets trapped in a different dimension or time period related to the supernatural and has to find her way back while dealing with the local supernatural threats there.
There are often plotlines where the reader is transported into the Supernatural universe and immediately runs into demon dean. Their relationship starts off rocky, with dean seeing the reader as an easy target or a nuisance. But as the story unfolds, they discover that they are linked in some way, perhaps by a prophecy or a shared past life. This leads to a journey of self - discovery for both of them as they figure out their relationship and their roles in the supernatural world.
In Supernatural fanfiction, a frequent plotline involving Sam and Bela Talbot is that of a reluctant partnership. Bela might drag Sam into one of her heists that ends up being more than she bargained for, and they have to face some terrifying supernatural entity together. Or perhaps Bela double - crosses Sam at first, but then realizes she needs his help to survive a situation. There are also plotlines where Sam tries to reform Bela, seeing some good in her that she doesn't even see in herself.
One common plotline is a female character getting pregnant unexpectedly, and the Winchester brothers having to protect her from supernatural threats because of the unborn child's special significance. For example, the child might be prophesied to have great power, attracting all kinds of evil forces.
One key element is the power dynamic. Henry, being a Winchester, has his own set of skills and knowledge, while Abaddon is a powerful demon. Their interactions often revolve around who has the upper hand at any given moment.
In fanfiction about Henry Abaddon's Daughter in Supernatural, a frequent theme is identity. She has to figure out who she is in relation to her father. Family drama is also common. Maybe she has a conflicted relationship with other family members who are also part of the Supernatural world. And love can be a theme too. She could fall in love with a character from the show, which would add an interesting dynamic to the story.
I'm not sure specifically which 'Henry Abaddon's Daughter' fanfiction in Supernatural you're referring to. There could be many different takes on this in the fanfiction world. Some might focus on her relationship with the main characters in the show, like how she might interact with Sam and Dean. Others could explore her backstory, her powers if she has any, and how she fits into the Supernatural universe.