  We analyze the number of independent chiral zero modes and the winding
numbers at the fixed points on $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$) orbifolds
with magnetic flux. In the case of $N=2$, we derive the index formula
$n_{+}-n_{-}=M/2+(-V_{+}+V_{-})/4=M/2-V_{+}/2+1$ by using the trace formula,
where $n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$
are the sums of the winding numbers at the fixed points on
$T^2/{\mathbb{Z}}_2$. We also obtain the formula
$n_{+}-n_{-}=M/N+(-V_{+}+V_{-})/(2N)=M/N-V_{+}/N+1$ for $N=3,4,6$ under an
assumption.
