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We investigate blow-up manifolds of ${T}^{2}/{\mathbb{Z}}_{N}(N=2,3,4,6)$ orbifolds with magnetic flux. First, we construct the and zero-mode wave functions on them more precisely. In particular, through an appropriate singular gauge transformation, winding numbers ${T}^{2}/{\mathbb{Z}}_{N}$ can be replaced localized curvature flux at orbifold fixed points. addition, since have no singularities, apply Atiyah-Singer index theorem to them; chiral number is given by total It also applied for process, then find that it consistent counting formula in M. Sakamoto et al. [Zero-mode zeros compactifications, Phys. Rev. D 102, 025008 (2020).]. Furthermore, shows additional degree freedom gives new zero modes. study their they correspond modes calculate Yukawa couplings.