  In this paper, we present a systematic investigation on simple inverse seesaw
models for neutrino masses and flavor mixing based on the modular $S^{}_4$
symmetry. Two right-handed neutrinos and three extra fermion singlets are
introduced to account for light neutrino masses through the inverse seesaw
mechanism, and to provide a keV-mass sterile neutrino as the candidate for warm
dark matter in our Universe. Considering all possible modular forms with
weights no larger than four, we obtain twelve models, among which we find one
is in excellent agreement with the observed lepton mass spectra and flavor
mixing. Moreover, we explore the allowed range of the sterile neutrino mass and
mixing angles, by taking into account the direct search of $X$-ray line and the
Lyman-$\alpha$ observations. The model predictions for neutrino mixing
parameters and the dark matter abundance will be readily testable in future
neutrino oscillation experiments and cosmological observations.
