Are you using a secure mail key to connect to inbound.att.net and outbound.att.net?

https://support.mozilla.org/en-US/questions/1293897

I cannot find where to do the following on TB. I think that is what your suggestion was.

Create a secure mail key Learn how to create a secure mail key from your mobile device, tablet, or computer. Have your User ID and password ready to sign in to myAT&T.

   Go to Profile > Sign-in info.
   Select the email account that you want to get a secure mail key for. (You’ll find a drop-down menu at the top if you have multiple accounts.) 
   Scroll to Secure mail key and select Manage secure mail key.
   If you have more than one email address, select the one you want to use.
   Select Add secure mail key.
   Enter a nickname for the secure mail key to make it easier to recognize.
   Select Create secure mail key.
   Select Copy secure mail key to clipboard. (Jot down your secure mail key, so you have it handy if you have to update an email app on several devices.)
       For security purposes, the secure mail key only shows until you select OK. 
       If you lose or forget the secure mail key, you can create new secure mail keys as needed.
   Select OK.
   Go to your preferred email app and replace the existing password with your secure mail key. (For an IMAP account, delete the existing password for both the IMAP and SMTP servers and replace them with your secure mail key.)

The instructions for creating a secure mail key apply to any mail client, not just TB, and must be done on the webmail site for your account. TB has no capacity to change or set passwords or keys - it only applies that which is established on your mail provider's site.

https://www.att.com/support/article/email-support/KM1240308

OK - I think I understand the term"secure mail key" which I believe is another term for creating a secure password. I have done that on the AT&T website and I can access my email from their website.

The problem I'm having is to get TB to recognize that new AT&T password. When I log in to TB and it ask for my password, I enter it and I get this error message.

Sending of password for user CarolJL@bellsouth.net did not succeed. Mail server inbound.att.net responded: Server error - Please try again later.

I have tried multiple times after I exit TB and later try to get it to recognize my password.

Help!

Did you delete the old passwords in Options/Security/Passwords/Saved Passwords, restart TB, and enter the secure key when prompted?

Yes I did