In this study, we demonstrate the efficacy of the Ultraviolet Imaging Telescope (UVIT) in identifying and characterizing white dwarfs (WDs) within the Milky Way Galaxy. Leveraging the UVIT point-source catalogue towards the Small Magellanic Cloud and cross-matching it with Gaia DR3 data, we identified 43 single WDs (37 new detections), 13 new WD+main-sequence candidates, and 161 UV bright main-sequence stars by analysing their spectral energy distributions. Using the WD evolutionary models, we determined the masses, effective temperatures, and cooling ages of these identified WDs. The masses of these WDs range from 0.2 to 1.3 M$_ odot $ and the effective temperatures (T$_ eff $) lie between 10000 K to 15000 K, with cooling ages spanning 0.1 to 2 Gyr. Notably, we detect WDs that are hotter than reported in the literature, which we attribute to the sensitivity of UVIT. Furthermore, we report the detection of 20 new extremely low-mass candidates from our analysis. Future spectroscopic studies of the extremely low-mass candidates will help us understand the formation scenarios of these exotic objects. Despite limitations in Gaia DR3 distance measurements for optically faint WDs, we provide a crude estimate of the WD space density within 1kpc of 1.3 times 10$^ $ pc$^ $, which is higher than previous estimates in the literature. Our results underscore the instrumental capabilities of UVIT and anticipate forthcoming UV missions such as INSIST for systematic WD discovery. Our method sets a precedent for future analyses in other UVIT fields to find more WDs and perform spectroscopic studies to verify their candidacy.