I'm not certain what was mean by "brings down messages" and "keeps coming" here; you're seeing duplicates of some sort? Messages are not eliminated? I'm going to make some guesses here, and some of the following might not apply to this case.
Some mail connections — IMAP, for instance — don't usually copy the messages from the server to the client, too. (You might already know that, of course.)
What does the Connection Doctor tool in Mail.app indicate about the connection? Valid and functional?
Does the option to repair (Rebuild) the folders involved clear this?
There are also cases where there are corrupt mail messages, and these can get stuck between the server and the client. If Charter has a web mail service available, that can sometimes be used to delete the problematic messages from the server.
What I meant by "brings down messages" and "keeps coming" is that so long as mac mail is open the same message will down load continuously every minute or so. After clearing out my mail on the provider server, I sent myself a test message. After opening mac mail, within 10 to 15 minutes I had about 30 copies of the same message in my in box.
What is a connection doctor and where do I find it? How do I rebuild/repair folders? I tried deleting all inbox folders and accounts and started over but problem persists.