How are you accessing your email? On a phone or a computer using a desktop client or what? Where are the alerts coming from?
I am accessing on my Mac laptop. An option came when I was in the Voice section of Xfinity Comcast to see notifications. I thought it was to see the phone calls coming into my house line and clicked yes. Turns out it was for email. Now I get small boxes that come in from top right and announce each email I get. I want to turn off the email notifications but can find no guidance on any of Comcast web support pages.
I don't have the phone service, so I'm going to move the thread over to Voice so that maybe someone else there can tell you how to change the Voice settings.