  We investigate an alternative approach to the correspondence of
four-dimensional $\mathcal{N}=2$ superconformal theories and two-dimensional
vertex operator algebras, in the framework of the $\Omega$-deformation of
supersymmetric gauge theories. The two-dimensional $\Omega$-deformation of the
holomorphic-topological theory on the product four-manifold is constructed at
the level of supersymmetry variations and the action. The supersymmetric
localization is performed to achieve a two-dimensional chiral CFT. The desired
vertex operator algebra is recovered as the algebra of local operators of the
resulting CFT. We also discuss the identification of the Schur index of the
$\mathcal{N}=2$ superconformal theory and the vacuum character of the vertex
operator algebra at the level of their path integral representations, using our
$\Omega$-deformation point of view on the correspondence.
