IOS – iPhone 7 is not showing notifications for a incoming messages in Messages application

The messages app on the Mac has it's own preferences. Check if you're iMessage account is set up there and has a password set – perhaps you deleted it through keychain. If that doesn't help remove it with the minus and re-add the account.

Often a hard reset of the device will fix problems. Powering off and back on doesn't do the same thing as it does for a computer - it's more akin to hibernate mode in that its drawing no power, but nothing (RAM etc) is cleared.

To do a hard reset, on iPhone 6s and below, press and hold Sleep and Home until the Apple logo appears. On iPhone 7 and higher, press and hold Volume Down and Home.