  We consider 1/4 BPS black hole solutions of ${\cal N}=2$ gauged supergravity
in $AdS_4$. The near horizon geometry is $AdS_2 \times S^2$ and supersymmetry
is enhanced. In the first part of the paper we choose a moment map, which
allows the embedding of this supergravity solution into a sugra theory with a
hypermultiplet. We then perform the s-wave reduction of this theory at the
horizon and determine the dilaton multiplet, which couples to both metric and
gravitino fluctuations. In the second part we work with Euclidean axial
$\mathcal{N}=(2,2)$ JT supergravity and show how to add gauged matter in form
of covariantly twisted chiral and anti-chiral multiplets. We demonstrate how to
reduce the on-shell action to boundary superspace. We compare both theories and
calculate the fourpoint function by integrating out gravitons, gravitini and
photons for the s-wave setting and by use of the Super-Schwarzian modes in the
JT theory.
