Herein, we report the syntheses, structure, Na-ion conductivity, and theoretical investigation of two moisture stable quaternary compounds, Na3ZnGaQ4 (Q = S, Se). These compounds are synthesized using high-temperature solid-state synthesis routes employing polychalcogenide flux or by metathesis reactions. The crystal structure of these compounds is built up of a three-dimensional (3-D) network of corner-shared supertetrahedral (T2) units, where two such 3-D networks are interlocked. The d-block metal and the main group metal, Ga, occupy the same crystallographic site with a 1:1 ratio, making it a rare form of building unit. Band structure calculations show that both the compounds are wide band gap semiconductors with band gaps of 2.25 and 1.61 eV, respectively, for Na3ZnGaS4 (I) and Na3ZnGaSe4 (II), which are slightly underestimated compared to experimentally determined band gaps of 3.0 and 1.90 eV, respectively. I and II possess ionic conductivities of 3.74 x 10-4 and 0.12 mS/cm with activation energies of 0.42 and 0.38 eV, respectively, at 30 °C. Interestingly, I shows a significantly high ionic conductivity of 0.13 mS/cm at 30 °C upon exposure to air, which could be due to water adsorption on the surface or occlusion in the grain boundaries. Assuming the vacancy-Assisted diffusion mechanism for ionic conductance, this difference is consistent with the difference on vacancy formation energies in these compounds, as predicted by DFT calculations. The bond valence sum map indicates that in both structures, the lowest energy diffusion path is one dimensional and it is along the c axis of the unit cell.