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

The Minimal Seesaw Model with a Modular $S_4$ Symmetry