Hi @mlaurenz.
Had this question not to long ago and the answer I got from Apple was that you cannot restrict which apple IDs can be used on a device. You can only allow or deny ALL apple IDs regardless of the type.
Cheers,
ES
I'm a Jamf School User, so not sure if this works the same. We lock the student devices so they are not able to change/edit/remove accounts with a Restrictions Profile. In School, its under Profiles > 9Create a new profile) > Restrictions > scroll to User modifications and turn off "Allow modifying account settings (E-mail, contacts, calendars, iCloud & iTunes Store)"
This locks the device to one Apple ID and doesn't allow the student's the ability to switch to a personal account.
Good Luck!
You cannot limit which AppleID signs in. Just whether any AppleID can be used or not at a blanket level. The best you could do is allow them to sign in, then lock it down. However you have no control over what they sign in with.