  The mass to luminosity ratio of the dwarf satellite galaxies in the Milky Way
suggests that these dwarf galaxies may contain substantial dark matter. The
dark matter at the dense region such as within or at the vicinity of the
centres of these dwarf galaxies may undergo the process of self annihilation
and produce $\gamma$-rays as the end product. The satellite borne $\gamma$-ray
telescope such as Fermi-LAT reported the detection of $\gamma$-rays from around
45 Dwarf Spheroidals (dSphs) of Milky Way. In this work, we consider particle
dark matter models described in the literature and after studying their
phenomenologies, we calculate the $\gamma$-ray fluxes from the self
annihilation of the dark matter within the framework of these models in case of
each of these 45 dSphs. we then compare the computed results with the
observational upper bounds for $\gamma$-ray flux reported by Fermi-LAT and Dark
Energy Survey (DES) for each of the 45 dSphs. The fluxes are calculated by
adopting different dark matter density profiles. We then extend similar
analysis for the observational upper bounds given by Fermi-LAT for the
continuum $\gamma$-ray fluxes originating from extragalactic sources.
