  In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], it
has been shown that center-of-mass-momentum-dependent two-body interactions can
be generated and tuned by Raman coupling the closed-channel bound states in a
magnetic Feshbach resonance. Here we investigate the universal relations in a
three-dimensional Fermi gas near such a laser modulated $s$-wave Feshbach
resonance. Using the operator-product expansion approach, we find that, to
fully describe the high-momentum tail of the density distribution up to
$q^{-6}$ ($q$ is the relative momentum), four center-of-mass-momentum-dependent
parameters are required, which we identify as contacts. These contacts appear
in various universal relations connecting microscopic and thermodynamic
properties. One contact is related to the variation of energy with respect to
the inverse scattering length and determines the leading $q^{-4}$ tail of the
high-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 related
to the variation of energy with respect to the range parameter and to the
kinetic energy of closed-channel molecules. Particularly, we find that the
$q^{-5}$ tail and part of the $q^{-6}$ tail of the momentum distribution show
anisotropic features. We derive the universal relations and, as a concrete
example, estimate the contacts for the zero-temperature superfluid ground state
of the system using a mean-field approach.
