I am an Aids Verifier. Am I entitled to wear the Operations ribbon or a different ribbon from the M-Department?

Those qualified as an ATON Verifier should wear the Operations Program ribbon/medal.  Bronze stars are used to denote qualification in multiple programs.  See AUXMAN Chapter 11, A.14.b.    Operations Program

This ribbon recognizes qualifications in the various operations program areas. Auxiliarists who qualify as an Auxiliary boat or air crew member, air observer, AtoN verifier, Coast Guard watchstander, Coast Guard boat crewman, Coast Guard boat engineer, or Auxiliary interpreter (Level A) may wear the Operations Program ribbon.