The quest for functional materials for the next generation of electronics plays a pivotal role in the postsilicon era, and two-dimensional layered semiconductors are at the core of this extensive research. In this work, we demonstrate that some members of the ${MA}_{2}{Z}_{4}$ family are candidates for high-efficiency optoelectronics. Through first-principles calculations, we find that the intrinsic electron mobility of ${MA}_{2}{\mathrm{N}}_{4}$ (where $M$ = {Mo, W} and $A$ = {Si, Ge}) layer materials reaches up to ${10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{V}\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ at liquid nitrogen temperature, and decreases as the temperature rises due to the enhanced electron-phonon scattering. Interestingly, the charge transport in these materials takes place purely along the intercalated transition metal nitride layer, so the surface adsorptions (impurities) or substrate interactions have nearly no effect on the carrier mobility due to the $A$-N bilayer protection, and the high electron mobility does not depend on the thickness of the sample. These features are distinct from other two-dimensional (2D) materials, such as silicene, black phosphorus, and indium selenide, and the 2D ${MA}_{2}{Z}_{4}$ family of materials are proposed as an outstanding candidate for field effect transistors and further studies.