Hi @Ivannaumov, welcome to our forum!
This is not possible to do with the settings in the device, since the Xperia XZ1 does not have a OLED display (Always on Display) or the setting that is available in the Xperia XZ2-series called "Ambient display" that will turn the screen on when receiving a notification.
You can always have a look in the Google Play store to see if there are any such applications available that will turn the screen on when you receive certain notifications in your device.
I hope that answers your question!
