Quasi two-zero texture in Type-II seesaw at fixed points from modular $A_4$ symmetry

We study a quasi two-zero neutrino texture based on a type-II seesaw model with modular $A_4$ symmetry to evade the cosmological bound on the sum of neutrino masses while keeping some predictability in the neutrino sector. Working on three fixed points for modulus, we discuss predictions of the model and show the allowed points satisfying the cosmological bound on neutrino mass from both CMB and CMB+BAO data.