I'm using the free Avast Mobile Security on a few of my devices, a phone, small tablet and a larger tablet and I rarely see any notifications.
My tablet generally only notifies me if I haven't done a scan in 7 days, which I dismiss.
In my Account - Settings - Notifications, I have all but one enabled (the junk one).
In the Protection section - I have the Automatic scan disabled.
If you can be more detailed as the the Notification it might help us to help you determine what Notification area it might be.