  We study 2d $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,4)$ theories derived from
compactifying class $\mathcal{S}$ theories on $S^2$ with a topological twist.
We present concise expressions for the elliptic genera of both classes of
theories, revealing the TQFT structure on Riemann surfaces $C_{g,n}$.
Furthermore, our study highlights the relationship between the left-moving
sector of the (0,2) theory and the chiral algebra of the 4d $\mathcal{N}=2$
theory. Notably, we propose that the (0,2) elliptic genus of a theory of this
class can be expressed as a linear combination of characters of the
corresponding chiral algebra.
