  We present detailed elemental abundances, radial velocity, and orbital
elements for Patchick~125, a recently discovered metal-poor globular cluster
(GC) in the direction of the Galactic bulge. Near-infrared high-resolution
($R\sim22,500$) spectra of two members were obtained during the second phase of
the Apache Point Observatory Galactic Evolution Experiment at Las Campanas
Observatory as part of the sixteenth Data Release (DR 16) of the Sloan Digital
Sky Survey. We investigated elemental abundances for four chemical species,
including $\alpha$- (Mg, Si), Fe-peak (Fe), and odd-Z (Al) elements. We find a
metallicity covering the range from [Fe/H] $= -1.69$ to $-1.72$, suggesting
that Patchick~125 likely exhibits a mean metallicity $\langle$[Fe/H]$\rangle
\sim -1.7$, which represents a significant increase in metallicity for this
cluster compared to previous low-resolution spectroscopic analyses. We also
found a mean radial velocity of 95.9 km s$^{-1}$, which is $\sim$21.6 km
s$^{-1}$ higher than reported in the literature. The observed stars exhibit an
$\alpha$-enrichment ([Mg/Fe]$\lesssim+0.20$, and [Si/Fe]$\lesssim +0.30$) that
follows the typical trend of metal-poor GCs. The aluminum abundance ratios for
the present two member stars are enhanced in [Al/Fe]$\gtrsim +0.58$, which is a
typical enrichment characteristic of the so-called `second-generation' of stars
in GCs at similar metallicity. This supports the possible presence of the
multiple-population phenomenon in Patchick~125, as well as its genuine GC
nature. Further, Patchick~125 shows a low-energy, low-eccentric ($<0.4$) and
retrograde orbit captured by the inner Galaxy, near the edge of the bulge. We
confirm that Patchick~125 is a genuine metal-poor GC, which is currently
trapped in the vicinity of the Milky Way bulge.
