Zee-Babu model in modular $A_4$ symmetry

We study a Zee-Babu model in a modular $A_4$ flavor symmetry, in which we search for several predictions such as phases, sum of neutrino masses, and neutrinoless double beta decay, satisfying neutrino oscillation data in a minimum framework of the charge assignments of modular weight. We perform $\Delta \chi^2$ analysis to get our results and find $\tau$ is localized nearby at one of the fixed points of $i\times \infty$ for both of normal and inverted mass hierarchies.