One interesting plotline is when Bella and Edward decide to raise Renesmee away from the vampire and werewolf communities for a while. This leads to a whole new set of adventures as they try to keep her safe and hidden. Also, there are fanfics where Bella has to choose between different versions of Edward from parallel universes. It makes for a very complex and engaging story.
In some fanfics, there could be a plotline where Bella discovers new powers, which changes the dynamic between her and Edward. Another plotline could be Renesmee growing up faster than expected and facing challenges that the original story didn't cover. For example, in a fanfic I read, Renesmee had to deal with other supernatural beings who were jealous of her unique abilities.
A common plotline is the exploration of Renesmee's relationships outside of her family. In some fanfics, she forms an unexpected friendship with a human or another supernatural being. Regarding Bella and Edward, there are stories where their relationship is tested by external forces in ways that are different from the original books. For instance, a powerful ancient vampire tries to break them apart for his own reasons. These plotlines add new dimensions to the Twilight universe in fanfics.
One common plotline is Edward and Bella having adventures in different time periods. For example, they might travel back to the era when Edward was human as Edward Masen. Another is them facing new supernatural threats together that are different from the ones in the original story. Sometimes, fanfiction might explore their relationship in an alternate universe where their roles are reversed, like Bella having vampire powers and Edward being the more vulnerable one.
One popular fanfic could be 'A Different Path'. It explores an alternate universe where Bella makes different choices early on. Another one might be 'Renesmee's Growth', which focuses on Renesmee's development in a unique way. There are also many on fanfic platforms that combine their relationships in new and interesting ways.
One interesting plotline could be Renesmee's journey as she grows up in a world full of vampires and werewolves. For example, she might struggle to find her place among the two groups and also in the human world she has a connection to. Another could be a story where Bella and Edward face a new threat that endangers their family and they have to rely on Renesmee's unique powers to overcome it.
I'm not sure who the absolute best - known authors are, but there are many talented writers in the fanfiction community. Some authors who have gained a following might be those who have been writing for a long time and have a large number of reviews on their stories. They often have unique takes on the Edward and Bella relationship and are able to create engaging storylines.
One possible plotline could be Renesmee's growth and her relationship with Edward as she discovers her unique abilities. Maybe she starts to show extraordinary powers early on, and Edward has to guide her in controlling them.
A plot could involve Renesmee's love life. Since she is a special being, finding a suitable partner would be difficult. It could be a story of her falling in love with a human who is initially afraid of her but gradually comes to accept her. Edward and Bella would be there to guide her through this new experience, while also being protective. Or perhaps a plot where Renesmee discovers a hidden power within herself that has been passed down from an ancient vampire ancestor, and she has to learn to control it with the help of Edward and Bella.
Maybe a plot where Renesmee has to face some sort of vampire - human conflict that her parents once faced, but in a different context. Since she is part - vampire and part - human, she could be a bridge between the two worlds and strive to bring peace. She could use her understanding of both sides to defuse tense situations.
Some fanfictions may revolve around alternate universes. In these stories, the relationship between Edward, Bella and Renesmee could be completely different. Maybe in one AU, Renesmee has different powers or they live in a world where vampires and humans co - exist more peacefully. Additionally, there are fanfictions that might focus on the emotional bonds within the family. How Edward and Bella's love for each other affects their relationship with Renesmee, and vice versa.
One interesting plotline could be Bella being reborn with some sort of supernatural power. For example, she might be able to control the elements. This would completely change the dynamic of her relationships in Forks. Another could be that she remembers her past life and uses that knowledge to avoid some of the dangerous situations she got into in the original story, like with the Volturi.
One possible plotline could be that Bella is kidnapped by a group who mistake her for someone else. They then realize their mistake but are in too deep to let her go easily. Another could be that a vampire from a rival coven kidnaps her to use as leverage against the Cullens.