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Abstract We compute the topologically twisted index for general N = 2 $$ \mathcal{N}=2 $$ supersymmetric field theories on ℍ 2 × S 1 $$ {\mathrm{\mathbb{H}}}_2\times {S}^1 $$ . We also discuss asymptotically AdS 4 magnetically charged black holes with hyperbolic horizon, in four-dimensional N = 2 $$ \mathcal{N}=2 $$ 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 ABJ M theories.