Creation of an Android Private app via the Managed Google Play Store in Intune
Navigate to https://intune.microsoft.com/#home (You will have to sign in with your abc123@case.edu account to gain access):

Click on Apps on the left-hand bar:

Click on Android under Platforms in the middle bar:

You will see a listing of the existing applications and what type they are.
Click on +Create at the top of the listing section:

Choose from the pull down the appropriate one you wish to create:

PLEASE NOTE: You can create a private app from inside of the Managed Google Play app.
The proper settings must be in place for the Managed Google Play app to work.
We will choose the Managed Google Play app for this instance:

Click the Select once you choose your listing:

Look to the left of the main blade. There are four icons. By default, you are put on the topmost one that looks like the Play icon. Choose the icon that looks like a lock:

This will put you into the Private apps area. You will see any current apps listed here.
Click on the large + at the bottom left of the screen:

Put in a title and then click on the Upload App button:

Click on the .apk file you want, verify it shows correctly under the File name section, then click on Open:

Once it is to your liking, click on the Blue Create button:

It may take some time for it to update to the above screen. The file needs to be uploaded, and this can take some time to process.
You will eventually be brought back to this screen or the Private apps screen. You will have the opportunity to edit the app should you wish to in the future.
PLEASE NOTE: If you have a previous app that has a new version and the developer didn’t change the package name, you cannot create a new instance using the same package name. You will have to update the existing or delete the old and do a new. If you update the existing, it will take a while for the system (Intune) to update the new name, etc. If that app was distributed it may also take some time for it to update to the device.