On the iPhone, go into voicemail and tap "Greeting". Record a few seconds of something and tap stop. Before you tap save, use iFuntastic or SFTP to navigate to /var/root/Library/Voicemail on your iPhone. You'll see a file called "Greeting. amr". This is the audio you just recorded. Delete that file and replace it with your custom message which should then be renamed to "Greeting.amr". Tap "Play" on the iPhone to verify your message works. If it plays, tap "Save" and your custom message will be uploaded to AT&T's servers.
How how how can that be??!! This is the year 2016, and I can’t set basic options like the number of rings! Actually I too want to turn off voicemail completely. I am aghast to read I don’t have a choice.

Step 3) Input the number of seconds that the iPhone should ring. Now type *11* and then enter the number of seconds that you want your device to ring before the call is sent to voicemail. If you want it to be 10 seconds, then you should now have the following on your phone app. *61*+123456789*11*10. Now you can place the call.
Updated in iOS: New features of Voicemail is how we can record or play it for later. Keep your iPhone updated to the latest version. and get Voicemail transcript features. Activation Step to Set up Voicemail on iPhone Form your iPhone home screen navigate Phone app then Tap on Voicemail. Tap Set Up Now. Now Enter the Password then Tap Done Remember – Enter password must be between 4 to 6 digits in length. Re-Enter the password again then Tap Done. Tap Custom to record a greeting. Would you want to use default Verizon greetings then tap (check) Defaults? Tap Record to begin.