tell her "proof or take it to the courts and prove it there. until such a time as you provide proof a child even exists that could remotely actually be his, do not contact again."

create a throw away gmail account. provide that account to the ex GF. inform her that she will be blocked on ALL other forms of communication. once proof is provided (if it is) then arrange to meet IN PUBLIC to get a DNA sample of the child's to compare to your SO.

proof likely won't be sent, but at least there is an avenue in the event she isn't lying about the child.

likely she is, because why didn't she go after support?