We report the detection of 21-cm absorption from foreground galaxies towards quasars, specifically z_gal = 0.3120 towards SDSS J084957.97+510829.0 (z_qso = 0.584; Pair-I) and z_gal = 0.3714 towards SDSS J144304.53+021419.3 (z_qso = 1.82; Pair-II). In both the cases, the integrated 21-cm optical depth is consistent with the absorbing gas being a damped Lyman-\alpha (DLA) system. In the case of Pair-I, strong Na I and Ca II absorption are also detected at z_gal in the QSO spectrum. We identify an early-type galaxy at an impact parameter of b ~ 14 kpc whose photometric redshift is consistent with that of the detected metal and 21-cm absorption lines. This would be the first example of an early-type galaxy associated with an intervening 21-cm absorber. The gas detected in 21-cm and metal absorption lines in the outskirts of this luminous red galaxy could be associated with the reservoir of cold H I gas with a low level of star formation activity in the outer regions of the galaxy as reported in the literature for z ~ 0.1 early-type galaxies. In the case of Pair-II, the absorption is associated with a low surface brightness galaxy that, unlike most other known quasar-galaxy pairs (QGPs) i.e. QSO sight lines passing through disks/halos of foreground galaxies, is identified only via narrow optical emission lines detected on top of the QSO spectra. Using SDSS spectra we infer that the emission lines originate within ~ 5 kpc of the QSO sight line, and the gas has metallicity [12+O/H] ~ 8.4 and star formation rate ~ 0.7-0.8 M_sun per yr. The measured 21-cm optical depth can be reconciled with the N(H I) we derive from the measured extinction (A_V=0.6) if either the H I gas is warm or the extinction per hydrogen atom in this galaxy is much higher than the mean value of the Small Magellanic Cloud. (Abridged)

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