Email

I have an email that ends in .net which is both Yahoo and att. On my smartphone I received an email from the parent company of Yahoo stating that my email would be discontinued unless I agree to Yahoo's terms. In the past just changing my At&T password took care of the problem. Now that won't work. Since I am an AT&T customer I don't want to have Oath, the parent company of Yahoo to have any info on my email or me. What do I do now?