  In this paper, we have studied the consequences of some representative
modular symmetry neutrino models for tri-resonant leptogenesis (which is
realized by having three nearly degenerate right-handed neutrinos). To be
specific, we have considered modular ${\rm A}^{}_4$, ${\rm S}^{}_4$ and ${\rm
A}^{}_5$ symmetry models that have a right-handed neutrino mass matrix
$M^{}_{\rm R}$ as shown in Eq.~(\ref{5}) which gives three degenerate
right-handed neutrino masses and consequently prohibits the leptogenesis
mechanism to work. For these models, we have considered two minimal ways to
generate the desired small mass splittings among the three right-handed
neutrinos: one scenario is to modify $M^{}_{\rm R}$ to a form as shown in
Eq.~(\ref{7}), while another scenario is to consider the renormalization-group
corrections for the right-handed neutrino masses. In the former scenario, for
the considered models, the observed value of $\eta^{}_{\rm B}$ can always be
successfully reproduced for appropriate values of $\mu$. But in the latter
scenario not all the considered models can successfully reproduce the observed
value of $\eta^{}_{\rm B}$.
