ABSTRACTWe utilize JWST NIRCam medium-band imaging to search for extreme redshift (z ≥ 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 six robust candidates, three of which have recently been spectroscopically confirmed. One of these three is the previously controversial z ≃ 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 zphot = 11.6 ± 0.2. We also detect two galaxies at z ≥ 12.5 including a newly-detected candidate in the imaging provided by the second NIRCam module (south-west of the HUDF) at zphot = 12.6 ± 0.6. We determine the physical properties of the six galaxies by fitting the 14-band photometry with Bagpipes. We find stellar masses of log (M⋆/M⊙) ≃ 7.5−8.7 and star-formation rates of $\log (\rm {SFR}/M_{⊙ }^{-1} \rm {yr}^{-1}) ≃ 0.3 - 5.0$. 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 ultraviolet luminosity function and cosmic star-formation rate density at z ≃ 11, supporting a gradual steady decline in the cosmic star-formation rate density out to at least z ≃ 15.