A series of quaternary selenides, NaxMGaSe4 (M = Mn, Fe, and mixed Zn/Fe), have been synthesized for the first time employing a high-temperature solid-state synthesis route through stochiometric or polychalcogenide flux reactions. Along with the selenides, a previously reported sulfide analogue, NaxFeGaS4, is also revisited with new findings. These compounds form an interpenetrated structure made up of a supertetrahedral unit. The electrochemical evaluations exhibit a reversible (de)intercalation of ∼0.6 and ∼0.45 Na-ions, respectively, from Na2.87FeGaS4 (1a) and Na2.5FeGaSe4 (2) involving Fe2+/Fe3+ redox when cycled between 1.5 and 2.5 V. Mössbauer spectroscopy of 1a shows the existence of a mixed oxidation state of Fe2+/3+ in the pristine compound and reversible oxidation of Fe2+ to Fe3+ during the electrochemical cycles. Na2.79Zn0.6Fe0.4GaSe4 possesses a reasonably high room temperature ionic conductivity of 0.077 ms/cm with an activation energy of 0.30 eV. The preliminary magnetic measurements show a bifurcation of FC-ZFC at 4.5 and 2.5 K, respectively, for 1a and Na3MnGaSe4 (4) arising most likely from a spin-glass like transition. The high negative values of the Weiss constants -368.15 and -308.43 K for 1a and 4, respectively, indicate strong antiferromagnetic interactions between the magnetic ions and also emphasize the presence of a high degree of magnetic frustration in these compounds.