What to do:
Turn off push notifications from apps. If you really need them then turn off preview of the content from your locked device.
Why do it?
What is available on your mobile screen without signing in?
Can a glance of your locked phone tell someone where your next appointment is and with who? Can he see the one-time-PIN that the bank just sent you, or your bank balance, or any other personally identifiable information?
Turning off previews will let the phone tell you that you have one unread message but will have no further details until you sign in with your PIN or fingerprint.