In this work, we implement $A_4$ modular invariance approach within the framework of type-III seesaw mechanism with $\rm U(1)_{B-L}$
as an additional gauge symmetry to the standard model (SM). The model includes SM particle spectrum
with extra $ \rm SU(2)_L $ triplet fermion $\Sigma_R$ and a scalar singlet $\rho$, which breaks the
$\rm U(1)_{B-L}$ symmetry. Fermion triplet participates in the seesaw mechanism to
give tiny mass to neutrinos. Hence, we are able to explain neutrino phenomenology, to name a few, sum of neutrino masses, reactor mixing angle etc. satisfying their present experimental 3$\sigma$ bound respectively. Also, we discuss leptogenesis and effective
electron neutrino mass parameter $\langle m_{ee} \rangle$ in neutrinoless double beta decay satisfying KamLAND-Zen bound.