Oauth question : regarding allowed and blocked user types

Been a long day and I'm not thinking straight as to what to google for.

I have set up socialite and have users been verified through oauth and then registering in my db.

I was doing some user testing and realized that I don't want just everybody to sign up. I did set the hd option so that limits the users to a certain domain. However! I don't want everybody with the whitelisted domain to be able to sign-in/sign-up.

Is this something controlled through a panel at google/github or do I have to run a filter test against known allowable users and then forgo the ability to allow users to sign-up.

Basically, Be able to ALLOW all teachers/staff access but verified by oauth DENY all students from being able to be verified by oauth

Thanks!