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We construct a successful model to explain the muon anomalous magnetic momentoriginated from Yukawa terms. Thanks to a modular $A_4$ flavor symmetry, thereare not any lepton flavor violations from the terms that would spoil the model.We also investigate a predictive radiative seesaw model including dark mattercandidate at favorable fixed points of $\tau=\omega,\ i$ obtained by recentanalysis of the stabilized moduli values from the possible configurations ofthe flux compactifications. In the result, we show our predictions on the DiracCP and Majorana phases, the neutrino masses through $\chi^2$ analysis. Then, wedemonstrate the allowed regions to satisfy the muon anomalous magnetic momentand the observed relic density of dark matter in terms of valid masseigenstates.

Muon $g-2$ and neutrino mass explanations in a modular $A_4$ symmetry