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We have built a lepton-specific next-to-minimal two-Higgs-doublet-portalvector dark matter model. The vector dark matter in the hidden sector does notdirectly couple to the visible sector, but instead annihilates into the hiddenHiggs bosons which decay through a small coupling into the CP-odd Higgs bosons.In this model, the Galactic center gamma-ray excess is mainly due to the 2-stepcascade annihilation with $\tau$'s in the final state. The obtained mass of theCP-odd Higgs $A$ in the Galactic center excess fit can explain the muon $g-2$anomaly at the 2$\sigma$ level without violating the stringent constraints fromthe lepton universality and $\tau$ decays. We show three different freeze-outtypes of the dark matter relic, called (i) the conventional WIMP dark matter,(ii) the unconventional WIMP dark matter and (iii) the cannibally co-decayingdark matter, depending on the magnitudes of the mixing angles between thehidden Higgs and visible two-Higgs doublets. The dark matter in the hiddensector is secluded from detections in the direct searches or colliders, whilethe dark matter annihilation signals are not suppressed in a general hiddensector dark matter model. We discuss the constraints from observations of thedwarf spheroidal galaxies and the Fermi-LAT projected sensitivity.

Hidden Higgs Portal Vector Dark Matter for the Galactic Center Gamma-Ray Excess from the Two-Step Cascade Annihilation, and Muon g-2