  We report JWST/NIRSpec spectra of three distant T-type brown dwarfs
identified in the Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of
Reionization (UNCOVER) survey of the Abell 2744 lensing field. One source was
previously reported as a candidate T dwarf on the basis of NIRCam photometry,
while the two other sources were initially identified as candidate active
galactic nuclei. Ultradeep, low-resolution 1-5 $\mu$m spectra confirm the
presence of molecular features consistent with T dwarf atmospheres, and
comparison to near-infrared spectral standards infers spectral classifications
of sdT1, T6, and T8-T9. The spectrum of the warmest source, UNCOVER-BD-1, shows
evidence of subsolar metallicity, and a fit to atmosphere models indicates Teff
= 1300 K and [M/H] ~ -1.0, making this one of the few examples of a
spectroscopically-confirmed T subdwarf. The spectrum of the coldest source,
UNCOVER-BD-3, places it near the T/Y dwarf boundary with Teff = 550 K, and we
identify features of CH$_4$, CO, H$_2$O, and likely PH$_3$ in the 3.5-5.0
$\mu$m band. Our analysis suggests that PH3 is favored over CO$_2$ in this
source, a possible indicator of subsolar metallicity. We estimate distances of
0.9-4.5 kpc from the Galactic midplane, and population simulations indicate
high probabilities of membership in the Galactic thick disk or halo. Our
simulations also indicate that there may be up to 7 T dwarfs and 5-6 L dwarfs
in the Abell 2744 field down to F444W = 30 AB mag, roughly half of which are
halo members. These results highlight the utility of deep JWST/NIRSpec
spectroscopy for identifying and characterizing the oldest metal-poor brown
dwarfs in the Milky Way.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics;Astrophysics of Galaxies