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We present the results from our 21‐cm absorption survey of a sample of five quasar–galaxy pairs (QGPs), with the redshift of the galaxies in the range 0.03 ≤ z  g ≤ 0.18, selected from the Sloan Digital Sky Survey (SDSS). The H  i  21‐cm absorption was searched towards the nine sightlines with impact parameters ranging from ∼10 to ∼55 kpc using the Giant Metrewave Radio Telescope (GMRT). 21‐cm absorption was detected only in one case, i.e. towards the quasar ( z  q = 2.625 SDSS J124157.54+633241.6)–galaxy ( z  g = 0.143 SDSS J124157.26+633237.6) pair with the impact parameter ∼11 kpc. The quasar sightline in this case pierces through the stellar disc of a galaxy having near solar metallicity [i.e. (O/H)+12 = 8.7] and star formation rate uncorrected for dust attenuation of 0.1 M  ⊙  yr  −1 . The quasar spectrum reddened by the foreground galaxy is well fitted with the Milky Way extinction curve (with an   A V    of 0.44) and the estimated H  i  column density is similar to the value obtained from 21‐cm absorption assuming a spin temperature ( T  S ) of 100 K.  In the remaining cases, our GMRT spectra provide upper limit on  N (H  i ) in the range  (10 17 –10 18 ) × T  S  cm −2  . Combining our sample with the   z ≤ 0.1  data available in the literature, we find the detectability of 21‐cm absorption with integrated optical depth greater than 0.1 km s −1  to be 50 per cent for the impact parameter less than 20 kpc. Using the surface brightness profiles and a well‐established relationship between the optical size and extent of the H  i  disc known for  nearby  galaxies, we conclude that in most of the cases of 21‐cm absorption non‐detection, the sightlines may not be passing through the H  i  gas (1σ column density of a few times 10 19  cm −2 ). We also find that in comparison to the absorption systems associated with these QGPs,   z  &lt; 1  damped Lyman‐α absorbers (DLAs) with 21‐cm absorption detections have lower Ca  ii  equivalent widths despite having higher 21‐cm optical depths and smaller impact parameters. This suggests that the current sample of DLAs may be a biased population that avoids sightlines through dusty star‐forming galaxies. A systematic survey of QGPs over a wider redshift range using a large sample is needed to confirm these findings and understand the nature of 21‐cm absorbers.

GMRT mini‐survey to search for 21‐cm absorption in quasar–galaxy pairs at z ∼ 0.1