Four new quaternary chalcogenides with the formula of Na(6)Zn(3)MIII2Q(9) (M-III = Ga, In; Q = S, Se) have been successfully synthesized for the first time. They are isostructural and crystallize in the monoclinic C2/c space group. As seen from their structures, they exhibit two opposite direction layers composed of the interconnection of countless (Zn/M-III)(10)Q(20) supertetrahedra (T-3-type) clusters, and then three coordination-type NaQ(n) units (n = 4-6) exist among the interlayers to bridge them together. Note that these T-3 clusters connect with each other by vertex-sharing to form the layers in the title compounds, which can be viewed as the first discovered examples in the known quaternary chalcogenides that only exhibit the tetrahedron-sharing T-3 clusters. Moreover, we have also systematically compared the structural differences of all the T-3-containing quaternary chalcogenides and the result shows that the title compounds possess the shortest interlayer spacing and more tilting T-3 cluster-built layers in comparison with other related compounds. The measured optical properties indicate that their optical bandgaps are in the range from 2.22 to 3.15 eV, respectively. The photoluminescence result shows that the title compounds have potential application prospects as blue and green light emitters in view of their obvious emission peaks centered at 463 and 541 nm. Electronic structures and density of states were also calculated by first-principles calculations and the results indicate that their optical bandgaps are mainly determined by the T-3 clusters.