Q: Apple Mail vs AT&T

My sub accounts for email w/ AT&T are set up and my wireless connection is fine but Apple Mail will not seem to get through using the passwords. What's worse is that I can't get past the constant popups to get into Apple Mail preferences to check to see if all is OK. It should be OK as I entered each sub acct. by hand and checked them. Not the first time this has happened and AT&T had to fix it last time and said ithe problem was Apple Mail which I tend to believe as Apple Mail has given me problems since I started using it and stopped using TB. I read some previous (2012) support issues before I posted this and saw that others thought it was AT&T but this is 2015 and I only have these problems with Apple Mail. I could certainly be incorrect and it is a problem at AT&T but they fixed Mail before and it worked very well for about a month. Help or advice either way would be appreciated as I love Apple products and just want this to work a little better. TCrowe