  We utilise JWST NIRCam medium-band imaging to search for extreme redshift ($z
\geq 9.5$) galaxy candidates in the Hubble Ultra Deep Field (HUDF) and the
additional pointing within the GOODS-South field provided by the second NIRCam
module. Our search reveals 6 robust candidates, 3 of which have recently been
spectroscopically confirmed. One of these 3 is the previously controversial $z
\simeq 12$ galaxy candidate UDF-22980 which is now detected in five JWST NIRCam
medium-band filters (F182M, F210M, F430M, F460M and F480M), efficiently
excluding alternative low-redshift solutions and allowing us to now report a
secure photometric redshift of $z = 11.6 \pm 0.2$. We also detect 2 galaxies at
$z \geq 12.5$ including a newly-detected candidate in the imaging provided by
the second NIRCam module (south-west of the HUDF) at $z = 12.6 \pm 0.6$. We
determine the physical properties of the 6 galaxies by fitting the 14-band
photometry with Bagpipes. We find stellar masses of $\log(M_{\star}/{\rm
{M_{\odot}}}) \simeq 7.5 - 8.7$ and star-formation rates of
$\log(\rm{SFR}/M_{\odot}^{-1} \rm{yr}^{-1}) \simeq 0.3 - 5.0$. Despite the
relatively small cosmological volume covered by the HUDF itself and the second
NIRCam module imaging, we find that the existence of these galaxies is fully
consistent with the latest measurements of both the UV luminosity function and
cosmic star-formation rate density at $z\simeq11$, supporting a gradual steady
decline in the cosmic star-formation rate density out to at least $z\simeq15$.
