Android Question Best practice "in-enterprise" Authoring, need advise.

Is it possible to "control" the gmail accounts that are allowed to my app in firebase? (I haven't found how, therefore my question)

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This is only authentication, in principle you check identification of the user (who am I).

Is it possible to "control" the gmail accounts that are allowed to my app in firebase? (I haven't found how, therefore my question)

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Besides authentication (who am I) you will have to come up with an authorization method (what am I allowed to do). You know the username of the user and what you could do is to do an arithmetic operation on it, which yields a "pin code". You can have this calculated the username to "pin code" by the program and only give it to that person as a "pin code" for his username. When the program start (for the first time) it calculated and check both calculated "pin code" (the user have something from you). Depending on your security requirements, you can add all kinds of extra protections.

Another method is to set up an authorization server.

Before develop a new wheel you may try an existing wheel: RADIUS
The protocol is open source. There are several implementations. E.g. FreeRADIUS
As you mentioned enterprise if you need support they also offer it in a certain price range.
If you want to test it they have documentation how to do it.
There is also a list with packages for several operating systems.