We propose matter wavefunctions on resolutions of $T^2/\mathbb{Z}_N$ singularities with constant magnetic fluxes. In the blow-down limit, the obtained wavefunctions of chiral zero-modes result in those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models, but the wavefunctions of $\mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixed points of $T^2/\mathbb{Z}_N$ orbifolds. Such blow-up effects change the selection rules and Yukawa couplings among the chiral zero-modes as well as the modular symmetry, in contrast to those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models.

19 pages, 2 figures, v2: published version