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Tucana-II (Tuc-II), a recently discovered and confirmed Ultra Faint DwarfSpheroidal galaxy, has a high mass to light ratio as well as a largeline-of-sight stellar velocity dispersion, thus making it an ideal candidatefor an indirect dark matter (DM) search. In this paper, we have analyzed nineyears of $\gamma$-ray data obtained from the \textit{Fermi}-LAT instrument fromthe direction of Tuc-II. The fact that a very weak significant $\gamma$-rayexcess ($2.2\sigma$) over the background of Tuc-II have been detected from thelocation of this galaxy. We have observed that this excess of $\gamma$-rayemission from the of location Tuc-II rises with longer periods of data. If WIMPpair annihilation is assumed for this faint emission, for $b\bar{b}$annihilation channel the test statistics (TS) value peaks at DM mass $\sim$ 14GeV 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 limitof the possible velocity weighted self-annihilation cross-section of the DMparticles (WIMPs) within Tuc-II by fitting the observed $\gamma$-ray flux withspectra expected for DM annihilation. The estimated upper limits of thecross-sections from Tuc-II are then compared with two other dwarf galaxies thatare considered to be good DM candidates in several studies. We have alsocompared our results with the cross-sections obtained in various populartheoretical models of the WIMPs to find that our results impose reasonabletight constraints on the parameter spaces of those DM models. In the concludingsection, we compared our results with the similar results obtained from acombined dSph analysis by the \textit{Fermi}-LAT collaboration as well as theresults obtained from the studies of DM in the dwarf galaxies by the majorground-based Cherenkov experiments.

Analysis of Fermi-LAT data from Tucana-II: Possible constraints on the Dark Matter models with an intriguing hint of a signal