iOS – When you reach the maximum 3 attempts, the option to Use Touch ID will no longer be available. If you lock and unlock your device using your passcode, the Use Touch ID option will reappear. You can still enter your password manually to proceed at any stage.
Android – When you reach the maximum 5 attempts, you will see a message that too many attempts have been made. You will then be able to wait a minute and then you can re-try the fingerprint scanner. You can still enter your password to proceed at any stage.