Abstract: This paper discussed the new constraints on thermally averaged dark matter annihilation cross section, based on the new in-depth analysis of the J-factor of Ursa Major III/UNIONS 1, and 15 years of Fermi-LAT data. In this talk, besides their new results, I will also discuss some basic calculations for the J-factor and the Test Statistic method, which plays important roles in Dark Matter Indirect Detection.