  We have computed superconformal partial wave for the mixed correlators
involving $J$, $\phi$ and $\phi^\dagger$, where $J$ is the superconformal
primary of 4D ${\mathcal N} = 2$ stress-tensor multiplet, $\phi$ and
$\phi^\dagger$ are chiral and anti-chiral scalars respectively in the channel
$\langle J J \phi \phi^\dagger \rangle$. We have used the superembedding
formalism and computed conformal partial wave corresponding to the exchange of
long multiplet using the supershadow approach. This study provides part of the
ingredients necessary for the study of conformal bootstrap for mixed correlator
in 4D ${\mathcal N} = 2$ superconformal field theories.
