I don't know with AT and T or other provider. But my local number and toll-free number provider provides me with an answering rules that can be configured using a phone or an online account. This way I can block/unblock/ numbers. Maybe it offers the same functionality. Check with your provider by calling customer service.
Ring up the sevice provider- the person who you pay the phone bills to.How do find the phone number on my wifes phone she had it changed"?