  We study the prediction for leptogenesis in two renormalizable supersymmetric
$SO(10)\times A_4$ modular models in which the neutrino mass is dominantly
generated by the type I seesaw mechanism. The evolution of the lepton
asymmetries are described in terms of the three-flavored density matrix
equations for three heavy Majorana neutrinos, where both vanishing initial
condition and thermal initial condition of the right-handed neutrinos are
considered. We also present an analytical approximation based on the Boltzmann
equations. We find regions of parameter space compatible with the measured
fermion masses and mixing parameters as well as the baryon asymmetry of the
Universe. The predictions for the light neutrino masses, the effective mass in
neutrinoless doble beta decay and the leptonic CP violation phases are
discussed.
