Schneider et al. (2020) presented the discovery of WISEA J041451.67-585456.7 and WISEA J181006.18-101000.5, which appear to be the first examples of extreme T-type subdwarfs (esdTs; metallicity <= -1 dex, T_eff <= 1400 K). Here we present new discoveries and follow-up of three T-type subdwarf candidates, with an eye toward expanding the sample of such objects with very low metallicity and extraordinarily high kinematics, properties that suggest membership in the Galactic halo. Keck/NIRES near-infrared spectroscopy of WISEA J155349.96+693355.2, a fast-moving object discovered by the Backyard Worlds: Planet 9 citizen science project, confirms that it is a mid-T subdwarf. With H_W2 = 22.3 mag, WISEA J155349.96+693355.2 has the largest W2 reduced proper motion among all spectroscopically confirmed L and T subdwarfs, suggesting that it may be kinematically extreme. Nevertheless, our modeling of the WISEA J155349.96+693355.2 near-infrared spectrum indicates that its metallicity is only mildly subsolar. In analyzing the J155349.96+693355.2 spectrum, we present a new grid of low-temperature, low-metallicity model atmosphere spectra. We also present the discoveries of two new esdT candidates, CWISE J073844.52-664334.6 and CWISE J221706.28-145437.6, based on their large motions and colors similar to those of the two known esdT objects. Finding more esdT examples is a critical step toward mapping out the spectral sequence and observational properties of this newly identified population.
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