In addition to the main three, some fanfiction might focus on secondary characters like Alice. Since she can see the future, she could play an interesting role in the love triangle. For example, she might see different outcomes depending on who Bella chooses and try to influence the situation in a way that benefits the Cullens as a whole.
Obviously, Bella, Edward, and Jacob are the main ones. Bella is at the center of the love triangle, so she's always a key focus. Edward with his brooding vampire allure and Jacob with his warm werewolf charm are also very popular to write about.
Edward Cullen is often a popular choice. His brooding nature and vampire abilities make for interesting storylines. Writers can explore his character further, like how he would react if he was reborn with different memories or emotions.
Jacob Black is also quite popular. His loyalty and his struggle between his love for Bella and his werewolf identity can add a lot of depth to a fanfiction. Another popular character could be Alice Cullen. Her ability to see the future can create interesting plot twists and turns in a story 'into the night' in the 'Twilight' world.
The main hero, of course. They are often the center of the action in the original story, so there's a lot of material to work with. You can explore their uncharted emotions or put them in new and challenging situations.
Kaguya and Miyuki are the obvious choices. Their complex relationship, filled with pride and unspoken feelings, offers a lot of material for fanfiction. Writers can explore their inner thoughts and the development of their relationship in different scenarios.
Renesmee is definitely a popular one. Since she is a new and unique character in the Twilight universe, there are a lot of possibilities to explore with her. Jacob is also popular as his relationship with Renesmee is quite complex. And of course, the Cullen family members like Edward and Bella still hold a lot of interest as they are central to the whole story.
Edward and Bella are still very popular in fanfiction, even in the context of forbidden love. Their original relationship in the Twilight series had elements of the forbidden, with Edward being a vampire and Bella a human. Writers often explore different scenarios where their love is even more restricted, like if there was a curse that forbade their union.
Jacob Black is definitely a popular choice. He has a complex character arc in the original series and fans often like to explore more of his backstory or his future in fanfics. His relationship with the other wolves and his feelings for Bella can be further delved into.
Edward, even though he is absent for a large part of 'New Moon', still has a big impact on the story. Fanfic might explore his time away, what he was thinking and feeling, and how his return would be different if the story was told from a different angle.
The main protagonist is often a popular choice. Their journey through love and the challenges they face can be explored in more depth. For example, if they have a complex backstory in the original 'operation true love', fanfiction can expand on how that affects their present relationships.
Naru is also very popular. Her strong - willed and sometimes tsundere personality provides great potential for exploring her relationships, especially with Keitaro. There can be many stories written about her slowly opening up her heart and showing her softer side.