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[Display omitted] • Novel Janus Monolayer 1T'-MoSF is found through theoretical calculations. • Janus Monolayer 1T'-MoSF has high energetic, mechanical, dynamical, and thermodynamic stability. • Janus Monolayer 1T'-MoSF exhibits significant anisotropy, and superior mechanical flexibility. Janus monolayers of transition-metal dichalcogenides (TMDs) have garnered significant attention in various scientific fields due to their exceptional physical properties. Among the known Janus monolayer TMDs, MoSX holds particular significance, with X typically representing chalcogen atoms. The successful synthesis of MoSH has pushed the boundaries of X beyond the conventional chalcogens. Nevertheless, it remains an open question whether other elements can also yield stable Janus monolayer MoSX. Herein, we employ theoretical methods to undertake a comprehensive evaluation of the stability of Janus monolayer MoSX (X = Li, Be, B, C, N, F, Na, Mg, Al, Si, P, Cl). The analysis of stability encompasses various aspects, including energetic, mechanical, dynamical, and thermodynamic features. Interestingly, our investigations have revealed the existence of a hitherto undiscovered stable 1T'-MoSF structure. Remarkably, this structure exhibits significant anisotropy, providing superior mechanical flexibility due to its low Young's modulus. In addition, despite the dynamical instability of 2H/1T-MoSN and the mechanical instability of 2H/1T-MoSC/Mg, they could potentially exist under specific conditions. This theoretical study not only provides insights into the structural characteristics and stability of novel Janus monolayer MoSX, but also extends the Janus monolayer MoSX family, which would be valuable to future applications of Janus TMDs. [ABSTRACT FROM AUTHOR]