[Jess~]

First of all, I have to commend you for calling out her bullshit!! I was literally smiling in pride when I read that part, and I think you should feel very proud of yourself as well.

I don't understand why they don't want you in their study group, but it seems to me like it's completely their loss. You know the material, they obviously don't if they need study groups so often. I understand how it must hurt to be left out, especially when there is absolutely no reason for that childish drama they're trying to start. But it's not too late to take back the power you "gave them" to make you feel bad.
I've always lived by "fake it until you make it", and if you fake confidence and apathy towards their immature bullshit, eventually they'll believe you don't care. They might try even harder to get to you then, but honestly, from the way they're acting, they're either just being extremely immature for no apparent reason or they're jealous of something you've got. Maybe it's as simple as the fact that you know the material and they don't.

Whatever the reason behind this nonsense, I am certain that there is nothing wrong with you.
Perhaps try to reach out to some completely separate people in that class? Usually there's a few students who, even far into the semester, don't have a little "group" in class and are kind of just the outliers. Maybe try asking some of those quiet kids if they want to study together. Or even just sit next to them and try striking up conversation.

Sometimes I feel like it's best to approach the people who seem less approachable. Of course that's not always right, but you can kind of tell when someone is only quiet because they're insecure and aren't exactly sure how to socialize.

I'm sorry you had to go through this BS, especially in college, but it's definitely not your fault. They have some unresolved issues and for some reason think that high school clique drama is still relevant. How pathetic.
Move on and show them they're not even worth your time.