Sony recently rolled out the 3.10 firmware update for the PlayStation 4 console. Among the new features introduced with this update are notification setting, which allows users to set alerts for game and event invitations; community activity; and changes to music settings.
Enable or Disable Pop-Up Notifications on the PS4
To control the pop-up settings, go to Settings and then select Notifications. Here you will be able to enable or disable the pop-up notifications for all available items.