How to receive call and force that call to ring indefinitely to the caller but not the receiver My ultimate goal is to handle incoming calls that are obviously robospam, in such a way so that the robocaller cannot detect that this is a valid phone number with a real human at the end (including voicemail). If the robospammer detects that it is a valid number, they will record it for future spams. So I want that number to ring and ring indefinitely, and not go to voicemail.  

Most importantly, even if they have prior knowledge that I have picked up and hung up, or they left voice mail in previous attempts at reaching a live human at this phone number, I still want to send the call to the "ring indefinitely" state, and not go to voice mail, such that the caller hears the ringing, but the receiving phone stops ringing. The reason is that eventually the robospam problem has increased to the extent that, by my current practice off simply allowing all of them to go to voicemail (e.g., flipping the phone over to trigger the proximity sensor logic which then pushes it to voicemail), means that I have the ever increasing burden of listening and deleting the voicemails that are obviously spam. And that is a waste of time and distracting.

So, is there a way to configure a Samsung Galaxy Note 8, under the AT&amp;T carrier, to allow me to ring indefinitely, and not go to voicemail, and not be answered with some automated message? I'm not interested in rooting the phone.

Various Contact and Phone Tools - Android App Overview - IzzyOnDroid has a listing of related apps, but none are exactly what I'm after.
What you want is mostly a carrier-specific circumstance, and less of an Android device one.  Though, some OEMs support the ability to turn off call forwarding via Call app settings:

Device > Apps > Phone > More settings > Call forwarding > Voice call.  Then, disable these three things: "Forward When Busy", "Forward When Unanswered" and "Forward When Unreached".  This option may not be available on your device.

If the above option isn't offered on your device, you will have to log onto or call AT&amp;T customer support to turn off voice mail for your account.

See: https://forums.att.com/t5/AT-T-Phone-Features/Turn-Voicemail-On-and-Off/td-p/3606949