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We have obtained closed-form analytical expressions for the electron dressed states, or interacting Floquet states, which are generated by the off-resonant coupling between photon and the electrons in  T’-MoS_2 (tilted MoS₂). We note that T’-MoS₂ is one of the most recently discovered two-dimensional lattices which demonstrates spin- and valley-dependent tilted and anisotropic Dirac energy subbands that depend on the external vertical electric field. We have investigated  the manner in which  all these bands are affected by the off-resonant dressing field of various polarizations. Specifically, linearly polarized light modifies the existing anisotropy of the electronic states and a circularly polarized field results in an alteration of the existing bandgap.  We believe that our results are important for applications in band structure Floquet engineering.