  In this paper, we incorporate the modular $S^{}_4$ flavor symmetry into the
supersymmetric version of the minimal type-I seesaw model, in which only two
right-handed neutrino singlets are introduced to account for tiny Majorana
neutrino masses, and explore its implications for the lepton mass spectra,
flavor mixing and CP violation. The basic idea is to assign two right-handed
neutrino singlets into the unique two-dimensional irreducible representation of
the modular $S^{}_4$ symmetry group. Moreover, we show that the
matter-antimatter asymmetry in our Universe can be successfully explained via
the resonant leptogenesis mechanism working at a relatively-low seesaw scale
$\Lambda^{}_{\rm SS} \approx 10^7~{\rm GeV}$, with which the potential problem
of the gravitino overproduction can be avoided. In this connection, we
emphasize that the observed matter-antimatter asymmetry may lead to a stringent
constraint on the parameter space and testable predictions for low-energy
observables.
