  We compute the topologically twisted index for general $\mathcal{N} = 2$
supersymmetric field theories on $\mathbb{H}_2\times S^1$. We also discuss
asymptotically $AdS_4$ magnetically charged black holes with hyperbolic
horizon, in four-dimensional $\mathcal{N} = 2$ gauged supergravity. With
certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find
precise agreement between the black hole entropy and the topologically twisted
index, for $ABJM$ theories.
