I have assignments that I do not want to be assigned to every classes. However, it does not seem as if Power School gives me this option. Am I wrong? Is there away to assign certain assignments to only one class instead of every class?
When creating assignments teachers get the option to choose the class to whom they want to assign it which can be one or more. You can refer to this document: Assignments for more details.
In case you don't see the option, you will need to reach out to your district's Designated Support Contact and inform them about the issue so that they can work with Powerschool Support and have a look at your setup to investigate further.