One possible reason could be that Paul represents a different kind of life for Bella. Maybe he is more down - to - earth compared to the often brooding Edward. Paul might offer a simpler and more straightforward relationship without all the supernatural drama that comes with Edward.
Edward might be initially shocked. He has always seen Bella as his own and this sudden change could be hard for him to accept. He could become withdrawn and moody, similar to how he was before Bella entered his life.
Edward would probably be very confused at first. He would try to understand why Bella would leave him for Rosalie. He might start to analyze all their past interactions, looking for signs that he missed. Eventually, he could become angry, not at Bella directly, but at the situation. He might also feel a sense of betrayal, not just from Bella but also from Rosalie in a way, since Rosalie is 'taking' Bella away from him.
It could be that there are external forces at play. Maybe there are other characters or some kind of dark secret in the fanfiction lore that forces Edward to leave Bella while she's pregnant. For example, there could be a threat from a rival group that says they'll harm Bella and the baby if Edward stays, and he thinks leaving will draw the danger away from them.
Edward might be initially shocked and heartbroken. He has been in love with Bella for a long time, so her leaving for Jasper would be a huge blow. He could become withdrawn and moody, brooding over what went wrong.
She could be heartbroken. After all, she's pregnant and the person she loves has left her. She might feel abandoned and alone, crying a lot and wondering why Edward would do such a thing.
Well, it could be that Bella decides to raise the baby on her own without Paul. She could focus on building a support network of friends and family. Another aspect could be that the werewolf or vampire community (depending on the context of the original story) has some sort of reaction to Bella's situation. For example, they might try to protect her from any threats that come her way because of the unborn child.
Well, at first, Edward would be in shock. He wouldn't believe that Bella actually left. Then, he would likely start to search for her frantically. He might go to all the places they used to go together, hoping to find her. His reaction could also be one of self - blame. He would think that it was all his fault, that he didn't protect her well enough or love her the right way. As time passes, he could become more resigned to the situation. But he would never really forget her. He might even try to keep an eye on her from a distance, just to make sure she's okay, even though she left him.
I'm not sure if there is a particularly popular one. Fanfiction varies greatly in popularity and it depends on different fan communities. Some fanfictions might gain a following in certain groups who enjoy exploring alternative storylines, but it's hard to say for sure without extensive research into the Twilight fanfiction world.
One possible reason could be that Bella discovers a different side of Jasper that she finds more appealing. Maybe Jasper shows a deeper understanding of her in some aspects that Edward lacks. For example, Jasper's past experiences might make him more empathetic towards Bella's own struggles in a way that Edward, with his own set of vampire characteristics, doesn't quite get.