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Carbon nitride two-dimensional (2D) materials are among the most attractive class of nanomaterials, with wide range of application prospects. As a continuous progress, most recently, two novel carbon nitride 2D lattices of C3N5 and C3N4 have been successfully experimentally realized. Motivated by these latest accomplishments and also by taking into account the well-known C3N4 triazine-based graphitic carbon nitride structures, we predicted two novel C3N6 and C3N4 counterparts. We then conducted extensive density functional theory simulations to explore the thermal stability, mechanical, electronic and optical properties of these novel nanoporous carbon-nitride nanosheets. According to our results all studied nanosheets were found to exhibit desirable thermal stability and mechanical properties. Non-equilibrium molecular dynamics simulations on the basis of machine learning interatomic potentials predict ultralow thermal conductivities for these novel nanosheets. Electronic structure analyses confirm direct band gap semiconducting electronic character and optical calculations reveal the ability of these novel 2D systems to adsorb visible range of light. Extensive first-principles based results by this study provide a comprehensive vision on the stability, mechanical, electronic and optical responses of C3N4, C3N5 and C3N6 as novel 2D semiconductors and suggest them as promising candidates for the design of advanced nanoelectronics and energy storage/conversion systems.