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We study $SU(4)_C \times SU(2)_L \times U(1)_R$ models with modular $A_4$symmetry that provide unified description of the quark and lepton sectorincluding the flavor structures. The models are distinguished by theassignments of the modular weight on matter superfields. We carry out numerical$\chi^2$ analysis and search for parameter sets that accomodate theexperimental results. We provide a benchmark point for each model to illustrateimplications of our models.

$SU(4)_C \times SU(2)_L \times U(1)_R$ models with modular $A_4$ symmetry