I'm not sure specifically if there is a fanfiction with exactly that premise. But given the vast world of fanfiction, it's very possible. It could be an interesting take on the characters, but also a rather strange one considering Ginny and Hermione are friends in the original story. Maybe in this fanfiction, the author has a unique backstory or reason for Ginny to be 'out to get' Hermione, like a misunderstanding or some new plot device.
In a fanfiction, Ginny could be out to get Hermione because of a prophecy or some sort of ancient magic that pits them against each other. Maybe there's a hidden aspect of their characters' destinies that was never revealed in the original series. For example, a prophecy that only one of them can fulfill a great task at Hogwarts, and Ginny, believing it should be her, decides to undermine Hermione.
In many fanfictions where Hermione confronts Ginny Weasley, it often stems from a conflict over a boy, like Harry. Hermione might feel that Ginny is being too forward or not taking Harry's feelings into account. For example, if Ginny is making big moves on Harry without considering how it affects his studies or his mental state, Hermione, being the practical and studious one, could confront her. It could also be about their different personalities clashing in the context of the wizarding world's social dynamics.
They are popular because they are both strong female characters. Ginny is brave and talented in Quidditch, while Hermione is extremely intelligent. Their different strengths make for interesting combinations in fanfiction stories.
Ron could be one of the main characters. Since he is Hermione's boyfriend and Ginny's brother, he might be caught in the middle of their conflict. He could try to play the peacemaker or end up taking sides, which would further complicate the situation.
Another storyline might involve Ginny and Hermione teaming up to solve a mystery within Hogwarts. Maybe there are strange disappearances of students and they use their combined skills, Ginny's Quidditch - related quick thinking and Hermione's vast knowledge, to get to the bottom of it. They might suspect a hidden chamber or a rogue spellcaster. They start by interviewing students and staff, gathering clues from different parts of the castle, and finally unmask the culprit.
Scorpius Malfoy (again, in a fictional author sense) could write some interesting Ginny and Hermione fanfictions. He might bring in his family's perspective and create stories where Ginny and Hermione have to interact with the Malfoy family in some way, perhaps to heal old wounds or to work together on a project for the betterment of the wizarding community.
In a fanfiction, it could be that Ginny is being too reckless. Hermione, being the more cautious one, is always worried about getting into trouble. If Ginny is constantly sneaking out or getting involved in dangerous adventures, Hermione might yell at her to stop putting herself and others at risk.
I really like the fanfic 'Magic and Unity'. In this story, Hermione and Ginny team up to create a new spell. It shows their intelligence and creativity. Their interactions are so well - written, and it also includes other beloved characters from the Harry Potter universe, which makes the whole story very rich and enjoyable.
It could also be related to a boy. If both Ginny and Hermione are interested in the same guy, say Harry Potter, Hermione might stand up to Ginny to assert her own feelings or to clarify some misunderstandings that Ginny has about her relationship with the boy. This can create a tense situation between them in the fanfiction.
Yes, there are quite a few. Some can be found on popular fanfiction websites like FanFiction.net and Archive of Our Own. You can search for 'Bill Weasley and Hermione' and then sort through the results based on ratings and reviews to find ones that are well - written.