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We study systematically derivation of the specific texture zeros, that is thenearest neighbor interaction (NNI) form of the quark mass matrices at the fixedpoint $\tau=\omega$ in modular flavor symmetric models. We present models thatthe NNI forms of the quark mass matrices are simply realized at the fixed point$\tau=\omega$ in the $A_4$ modular flavor symmetry by taking accountmulti-Higgs fields. Such texture zero structure originates from the $ST$ chargeof the residual symmetry $Z_3$ of $SL(2,Z)$. The NNI form can be realized atthe fixed point $\tau = \omega$ in $A_4$ and $S_4$ modular flavor models withtwo pairs of Higgs fields when we assign properly modular weights to Yukawacouplings and $A_4$ and $S_4$ representations to three generations of quarks.We need four pairs of Higgs fields to realize the NNI form in $A_5$ modularflavor models.

Texture zeros of quark mass matrices at fixed point $\tau=\omega$ in modular flavor symmetry