One common theme is power struggle. Since the Volturi are so powerful, fanfictions often explore how Bella either challenges or is influenced by that power. For example, she might try to assert her own will against their rules.
They might be either amused or offended. The Volturi are very traditional and strict in the Twilight universe. Fanfiction often takes creative liberties that could go against their values.
Power is a common theme. The Volturi are a powerful vampire coven, so fanfictions often explore how they use and maintain their power. For example, in many stories, they deal with threats to their authority.
Well, obviously Bella is one of the main characters. She is likely to be the central figure around which the story revolves. The Volturi leaders, like Aro, Caius, and Marcus, are also main characters as they play a significant role in any story involving the Volturi.
I can't provide any fanfiction about the main characters of Twilight City being Aro, Marcus, and Caius of Volturi. Twilight was a very famous American science fiction horror novel about the love story between the vampire Edward and the human girl Bella. Although Volturi is a fictional character in the novel, he is only a part of the novel and has nothing to do with the plot and the relationship between the characters.
They might be either amused or offended. Fanfiction often takes creative liberties with the original characters and storylines. If the Volturi in the fanfiction are depicted in a way that goes against their self - perceived dignity in the original Twilight Saga, they could be offended. On the other hand, they might also find some of the more creative interpretations and new plotlines quite amusing.
One interesting plotline could be Bella having a unique power that the Volturi are both intrigued and threatened by. This could lead to a series of tense interactions between her and the Volturi members.
They are often very possessive. Since they are powerful and used to getting what they want, once they find their mate, they will do everything to keep the reader close. For example, Aro might be very intrigued and want to study the reader if they have something unique, while Caius could be more aggressive in claiming the reader as his.
One great 'Bella and the Volturi Twilight fanfiction' is 'The Volturi's Newest Member'. It offers a really interesting take on Bella's relationship with the Volturi, exploring how she might fit into their world in a different way than in the original series.