We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point tau =omega in modular flavor symmetric models. We present models that the 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 account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry Z_3 of SL(2, Z). The NNI form can be realized at the fixed point tau = omega in A_4 and S_4 modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings 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 modular flavor models.