  We propose, following the AGT correspondence, how the $\mathcal{W}^{\,
para}_{N, n}$ ($n$-th parafermion $\mathcal{W}_N$) minimal model characters are
obtained from the $U(N)$ instanton counting on ${\mathbb {C}}^2/{\mathbb
{Z}}_n$ with $\Omega$-deformation by imposing specific conditions which remove
the minimal model null states.
