How I cat mute the ringtone of Phone application during handling of incoming call from my program?

Typical scenario:
My program handles specific bluetooth hardware that have a button.
When incoming call comes I press the button and phone stops ringing. The call waits for answer. I don't want to reject the call from bt hardware.

There's an on-screen button that looks like a speaker with a red line over it when theres a call coming in, if thats what you're looking for

No, I think the OP is looking for a way to do this programmatically.