  We provide a systematic way of dimensional reduction for $(4+2n)$-dimensional
$U(N)$ supersymmetric Yang-Mills (SYM) theories ($n=0,1,2,3$) and their
mixtures compactified on two-dimensional tori with background magnetic fluxes,
which preserve a partial ${\mathcal N}=1$ supersymmetry out of full ${\mathcal
N}=2,3$ or $4$ in the original SYM theories. It is formulated in an $\mathcal
N=1$ superspace respecting the unbroken supersymmetry, and the four-dimensional
effective action is written in terms of superfields representing $\mathcal N=1$
vector and chiral multiplets, those arise from the higher-dimensional SYM
theories. We also identify the dilaton and geometric moduli dependence of
matter K\"ahler metrics and superpotential couplings as well as of gauge
kinetic functions in the effective action. The results would be useful for
various phenomenological/cosmological model buildings with SYM theories or
D-branes wrapping magnetized tori, especially, with mixture configurations of
them with different dimensionalities from each other.
