One common theme is family dynamics. Since it's about Bella's sister, it often explores how the sister fits into the family structure, especially with Bella being so central in the original Twilight story. Another theme is love triangles. Just like in the original, but now with the sister involved in some way.
The sister could have a big impact. Suppose she has a gift of reading minds like Edward. She might be able to tell if Edward has any hidden motives towards Bella. If she senses something wrong, she'll surely try to break them up. But if she approves of Edward, she could actually be a great confidante for both of them, and help them communicate better when they have misunderstandings.
There could be other minor characters from Forks that get more spotlight in these fanfictions. For instance, the classmates of Bella's little sister who start to notice that there's something strange about her. They might become curious and start to dig deeper into the secrets of the town, which then draws in the vampires and werewolves.
I really liked a fanfic where Bella's twin sister was a werewolf. It added a whole new layer to the story. Instead of being drawn to the Cullens like Bella, she was more involved with the werewolf pack. It explored how she tried to keep her identity a secret from Bella at first, which led to some really tense and exciting moments.
A common trope is the twin having a different supernatural ability. For example, she might be able to control the elements while Bella has her mind - shield. Another is the love triangle, but instead of Edward - Jacob - Bella, it's between different characters involving the twin. Often, the twin also has a secret she's keeping from Bella which drives the plot.
Love and friendship are also common themes. The baby sister may find love among the supernatural beings or form strong friendships. For example, she could become friends with some of the werewolves while also having a connection with the Cullens. It adds a new layer to the existing relationships in the Twilight world.
Some fanfictions might introduce new characters that become popular. For instance, a new vampire who befriends the little sister. This vampire could have a different set of powers or a unique backstory that makes them stand out. Also, other members of the Cullen family, like Alice, could have a closer relationship with the little sister in the fanfiction, which makes her a popular character in this new narrative.
Her relationship with Bella would likely become more complex. As a vampire, she would have different needs and instincts. She might be more protective of Bella in a way that Bella doesn't understand at first. For example, she could sense danger towards Bella that a human wouldn't notice. But at the same time, Bella might be a bit afraid of her sister's new vampire nature, which could create some tension between them.
The baby sister might also attract the attention of other supernatural beings. If she has an alluring scent like Bella, it could draw vampires or werewolves towards her. This would force Bella to take on a protective role and might lead to new alliances or battles in the Twilight universe. For example, the Cullens and the werewolves might have to work together more closely to keep the baby sister safe.
Well, in some of these fanfictions, Bella's little sister might have unique powers. For example, she could be able to communicate with animals in a way that no one else in the Twilight world can. This would lead to all sorts of adventures, like helping the Cullens avoid danger by getting warnings from forest creatures.