With Teaching assistant access, you can add students to the class only if they already have an account on Sowiso platform. Only Teachers can add Students who don't yet have accounts (learn how to invite new students here here).
To do this, go to the Teacher tab, and then to Users.
On the left side, you will see the list of Teachers and Students that are already in the class. You can add new Students by searching for them in the search bar on the right side of your screen.
To add them, click on the plus next to their name. To remove them, click on the trash can symbol.