Coherent atomic systems, e.g., resonantly cold atomic gases within which electromagnetically induced transparency (EIT) operates, have recently received great attention, because of their remarkable scientific properties and pivotal implications. Light behavior in such systems governed by various potentials is a new and interesting research focus, but missing literally report on two-dimensional (2D) localized gap modes in coherent atomic systems loaded on optical lattices. We survey such issue in a coherent atomic gas inside where the EIT turns on, trapped by 2D optical lattices—constituted by counter-propagating far-detuned Stark laser fields, in the framework of nonlinear Schrödinger equation derived from Maxwell-Bloch equations. Using the linear stability analysis and direct perturbed evolution we address the formation, property, and stability of 2D localized gap modes of two types, gap solitons and gap vortices, in forbidden band gaps of the underlying linear Bloch-wave spectrum. The former mode is fundamental gap solitons, and the latter belongs to higher-order gap solitons with embedded topological charge. Our results are helpful not only for in-depth understanding of soliton dynamics in coherent atomic ensemble loaded on periodic potentials, but also for laying the groundwork for forthcoming applications in optical communications and quantum information processing. © 2021 Elsevier B.V.