Thanks for that info and choosing the Apple Support Communities. Based on what you stated, it seems you are experiencing issues with notifications on your iPhone. First, make sure your iPhone is up to date, as the updates contain stability fixes that can resolve issues like yours, as well as important security updates to keep your iPhone safe.
Next, check your notifications settings at Settings > Notifications and then restart your device as iOS clears cached data and does other system optimizations when you turn your device off and on. Then test your issue again.