In some fanfictions, Edward's past as a vampire might come back to haunt him in relation to his role as a father. For example, an old enemy might target his child to get back at him. Or, he might have to come to terms with his own family's views on his single - fatherhood. His family could be either very supportive or have some reservations, and this can create a lot of drama and interesting story developments within the fanfiction.
Often, there could be a plot where Edward's child has some special ability or power, and he has to figure out how to help the child control it. And at the same time, there might be a love interest for Edward who has to accept both him and his role as a single father. Another plotline could be Edward trying to give his child a normal life despite the supernatural elements around them. He might enroll the child in a regular school and deal with the reactions of other humans when they start to notice something different about the family.
One common plotline is a love triangle where the female character, often Bella, is torn between Edward and Jacob. The fanfiction might explore different outcomes of this triangle, like her choosing Jacob instead of Edward which is a big deviation from the original story.
One common plotline is that he uses his military knowledge to protect the town from other supernatural threats. Maybe there are rogue vampires or werewolves causing trouble, and Edward steps in with his military - trained strategies to keep everyone safe.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of Twilight - related fanfictions, and you can use the search filters to specifically look for ones involving a single father Edward. Another option is FanFiction.net, though the content there may vary more in quality.
One common plotline is that Bella tries to find a way to get Edward back. She might go on a journey to discover something about herself or the vampire world that she thinks will make him return. Another is that she leans more on her friendship with Jacob and the werewolf pack for support. Sometimes, she also discovers new powers or abilities within herself as she copes with the loss.
Another common theme is the exploration of Edward's vampiric nature. Fanfic writers might focus on how he deals with his thirst for blood while being in love with a human, or how his vampiric abilities influence his relationships.
One interesting plotline could be Carlisle training Edward and Bella to better control their vampire powers. This would involve a lot of interaction between the three characters, with Carlisle using his experience to guide them. Another could be them facing a new vampire threat together, where Carlisle's leadership, Edward's abilities, and Bella's unique perspective as a former human come into play.
One possible plotline could be James Potter struggling to balance his work as a wizard (maybe he has a job at the Ministry) and taking care of his young child. For example, he might have to take the kid to work on some occasions and there would be all sorts of comical or heartwarming interactions with his colleagues. Another plotline could be him teaching his child magic for the first time, like when the child first shows signs of magic and James has to figure out how to be a good teacher and father at the same time.
One common theme is the exploration of Edward's new perspective. Since he's blind, he has to rely on different things, like his other enhanced vampire senses. This often leads to a deeper understanding of himself and his relationship with Bella.
One common theme is the exploration of a different kind of relationship dynamic. Since it's a female - centered view on Edward, often the power balance and emotional connection are re - examined. Another theme is the expansion of the vampire world. Fanfictions might introduce new vampire abilities or social structures related to Edward. Also, themes of self - discovery for the female character are common as she navigates her relationship with a complex character like Edward.
Love is a very common theme, just like in the original series. The intense, all - consuming love between Edward and Bella is often explored further in fanfiction. It might show different scenarios where their love is tested or strengthened.