  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.
