Here to help. I know it is important for your to be notificied about all your messages. When did this start happening? Are you still receiving your messages? Have you been able to power the phone off and on ? Keep us posted.
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Open settings, select notifications, select voicemail/calls, turn BADGES to on. The little red circle is called a badge.
Only get phone. Not voicemail phone. Phone shows badges on and a missed call shows the dot.
Are you getting new messages or is your mailbox full? As long as your badges are on under Phone in notifications then all badges under the phone app should work. You can try resetting your phone to see if that helps...and restore if all else fails. But outside of making sure the badges are on I'm not sure of a fix. And I'm assuming you are out of the warranty period...but if not you can always contact Apple to get them to troubleshoot and repair if they deem something is wrong and it's covered.