  Tucana-II (Tuc-II), a recently discovered and confirmed Ultra Faint Dwarf
Spheroidal galaxy, has a high mass to light ratio as well as a large
line-of-sight stellar velocity dispersion, thus making it an ideal candidate
for an indirect dark matter (DM) search. In this paper, we have analyzed nine
years of $\gamma$-ray data obtained from the \textit{Fermi}-LAT instrument from
the direction of Tuc-II. The fact that a very weak significant $\gamma$-ray
excess ($2.2\sigma$) over the background of Tuc-II have been detected from the
location of this galaxy. We have observed that this excess of $\gamma$-ray
emission from the of location Tuc-II rises with longer periods of data. If WIMP
pair annihilation is assumed for this faint emission, for $b\bar{b}$
annihilation channel the test statistics (TS) value peaks at DM mass $\sim$ 14
GeV and for $\tau^{+}\tau^{-}$ annihilation channel it peaks at DM mass 4 GeV.
It is then called for an estimation of the $95\%$ confidence level upper limit
of the possible velocity weighted self-annihilation cross-section of the DM
particles (WIMPs) within Tuc-II by fitting the observed $\gamma$-ray flux with
spectra expected for DM annihilation. The estimated upper limits of the
cross-sections from Tuc-II are then compared with two other dwarf galaxies that
are considered to be good DM candidates in several studies. We have also
compared our results with the cross-sections obtained in various popular
theoretical models of the WIMPs to find that our results impose reasonable
tight constraints on the parameter spaces of those DM models. In the concluding
section, we compared our results with the similar results obtained from a
combined dSph analysis by the \textit{Fermi}-LAT collaboration as well as the
results obtained from the studies of DM in the dwarf galaxies by the major
ground-based Cherenkov experiments.
