This is an issue that has ocurred to others. Cox reported in February, 2021 that it appears to be a notification flag on the vendor Admin side of a user's Forum profile that sometimes gets "stuck" on a notification. The vendor's resolution was simply to reset the flag to zero.
Contact firstname.lastname@example.org and ask them to have their vendor reset your Forum notification flag.
Alerts on your Cox Account page or the Forum? I think the keyword is "bell" and the Cox Account page has the bell.
These are not notifications, alerts, warnings, ding-a-lings or anything useful. These circles are just intrusive sales pitches. On my page, I have 2 red circles: 1 to upgrade my Internet & 1 to purchase Cox Complete Care. Cox designed these so you can't get rid of 'em. If I click 1, there will still be 2 on my page. It's just unscrupulous click bait.
Ah, I mis-read OP's post. Yes, the red circle in the bell on the account page does seem to be a permanent fixture. It's just background to me now. I had forgotten it was even there. But, if you ever get a red Forum notification circle again that you can't get rid of, contact Cox because they know how to clear it now.