Welcome to the Community. QuickBooks Online is a hassle-free program that simplifies the way you manage your transactions. I'll be happy to point you in the right direction so you can achieve your QuickBooks goals with ease.
I can see the benefit of being able to add a class to the auto-posting fees for QuickBooks payments. Since this feature isn't available, I recommend sending feedback about this to our engineers. You can do this by clicking the Gear icon and looking for Feedback. Product enhance are largely based on the feedback we get from users like you. In the meantime, I encourage you to check out this helpful article that shows you how to: