  We study a scotogenic extension of the minimal gauged $L_{\mu}-L_{\tau}$
model, including three right-handed singlet fermions and a scalar doublet all
odd under an in-built $Z_2$ symmetry to explain the anomalous magnetic moments
of the muon, CDF-II W-mass anomaly, and the 95 GeV excess reported by the CMS
collaboration. While the minimal model can successfully explain the muon
$(g-2)$ and CDF-II W-mass anomalies, the required diphoton signal strength for
the 95 GeV scalar, together with that of the SM Higgs, can not be obtained in
the minimal model. The same can, however, be explained by incorporating one
additional scalar doublet whose only role is to contribute radiatively to
diphoton decay modes of the light, neutral scalars. Due to the scotogenic
extension, the model remains consistent with the observed properties of light
neutrinos and dark matter in the Universe.
