Neutrinoless double-beta decay is a predicted beyond Standard Model process that could clarify some of the not yet known neutrino properties, such as the mass scale, the mass hierarchy, and its nature as a Dirac or Majorana fermion. Should this transition be observed, there are still challenges in understanding the underlying contributing mechanisms. We perform a detailed shell model investigation of several beyond Standard Model mechanisms that consider the existence of right-handed currents. Our analysis presents different venues that can be used to identify the dominant mechanisms for nuclei of experimental interest in the mass region (\(^{124}\)Sn, \(^{130}\)Te, and \(^{136}\)Xe). It requires accurate knowledge of nine nuclear matrix elements that we calculate in addition to the associated energy-dependent phase space factors.