I have a couple of guesses for what this could be, and I'm going to provide you with a couple links to help you troubleshoot this issue further. The first thing I would try for troubleshooting would be to sign out of every instance of the iTunes account possible in all of your devices and then try to sign in to them again. Next, follow these troubleshooting steps on your computer to attempt to stop that prompt from coming up when attempting to download:
It's also possible that you have two step verification turned on for your iTunes account. There is an article about that right here:
If you do have two step verification turned on and are having trouble signing in with it turned on, you will need to reference this article:
Hope that helps. Thanks for coming to the Apple Support Communities!