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In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], ithas been shown that center-of-mass-momentum-dependent two-body interactions canbe generated and tuned by Raman coupling the closed-channel bound states in amagnetic Feshbach resonance. Here we investigate the universal relations in athree-dimensional Fermi gas near such a laser modulated $s$-wave Feshbachresonance. Using the operator-product expansion approach, we find that, tofully describe the high-momentum tail of the density distribution up to$q^{-6}$ ($q$ is the relative momentum), four center-of-mass-momentum-dependentparameters are required, which we identify as contacts. These contacts appearin various universal relations connecting microscopic and thermodynamicproperties. One contact is related to the variation of energy with respect tothe inverse scattering length and determines the leading $q^{-4}$ tail of thehigh-momentum distribution. Another vector contact appears in the subleading$q^{-5}$ tail, which is related to the velocity of closed-channel molecules.The other two contacts emerge in the $q^{-6}$ tail and are respectively relatedto the variation of energy with respect to the range parameter and to thekinetic energy of closed-channel molecules. Particularly, we find that the$q^{-5}$ tail and part of the $q^{-6}$ tail of the momentum distribution showanisotropic features. We derive the universal relations and, as a concreteexample, estimate the contacts for the zero-temperature superfluid ground stateof the system using a mean-field approach.

High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance