One great fanfiction could be where Edward and Bella's relationship is explored more deeply in a different vampire society setting. For example, they might be in a vampire clan that has unique rules about human - vampire relationships.
Love is a very common theme. Their intense, often obsessive love for each other is a central part of most fanfictions. Another theme is the struggle between Bella's humanity and the vampire world she's drawn into. Also, the idea of family, like Edward's vampire family and how Bella fits into it.
A common theme is the 'what - ifs'. What if Bella had chosen Jacob instead? Fanfictions often explore this alternative storyline and how it would affect the vampire - human relations in Forks. It can be really interesting to see how the characters develop in this different scenario.
Love against all odds is a very common theme. Since they are from different species, there are a lot of obstacles in their relationship. For example, in many fanfictions, Bella has to control her vampire instincts around Edward, which adds a layer of tension.
The main characters are Edward, who is a vampire, and Bella, who is a human. Edward is often depicted as mysterious, brooding, and having a strong sense of protection towards Bella.
Often, other vampire clans that oppose Bella's transformation can be the main antagonists. They might see her as a threat to the vampire world order. For example, a traditionalist clan that believes humans should not be turned so easily could try to harm Bella or drive her away from Edward.
One common theme is the exploration of their eternal bond. Since they are vampire mates, their connection is supposed to last forever, and many fanfictions focus on how they maintain and strengthen this bond. Another theme is the challenges they face due to their different natures. Bella was once human, and becoming a vampire brings a whole new set of issues. Also, the theme of protecting each other and their family is quite common. They are mates, so they will do anything to keep each other safe.
Another common theme is the struggle between the vampire and human worlds. There are often conflicts arising from the differences in their natures, values, and lifestyles. Fanfiction writers usually show how Edward and Bella deal with these differences and try to find a balance between the two worlds.
I'm not sure if there is such a specific fanfic. There are countless fanfics out there, and while the 'Twilight' series has a large fanfic community, this particular combination seems rather unorthodox. It might exist in the vast realm of fan - created works, but it's not a common or widely - known trope within the official 'Twilight' lore.
A common plot is the exploration of their relationship in different settings. For instance, they might travel to a new place where vampire - human relationships are more accepted or more dangerous. This could lead to them facing new challenges together, like dealing with local vampire clans or human hunters who are aware of their presence. It also gives room for more character development as they adapt to new environments and situations.