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Discovery of an X-ray Emitting Contact Binary System 2MASS J11201034$-$2201340

We report the detection of orbital modulation, a model solution, and X-ray properties of a newly discovered contact binary, 2MASS J11201034$-$2201340. We serendipitously found this X-ray point source outside the error ellipse when searching for possible X-ray counterparts of $γ$-ray millisecond pulsars among the unidentified objects detected by the {\it Fermi Gamma-ray Space Telescope}. The optical counterpart of the X-ray source (unrelated to the $γ$-ray source) was then identified using archival databases. The long-term CRTS survey detected a precise signal with a period of $P=0.28876208(56)$ days. A follow-up observation made by the SLT telescope of Lulin Observatory revealed the binary nature of the object. Utilizing archived photometric data of multi-band surveys, we construct the spectral energy distribution, which is well fitted by a K2V spectral template. The fitting result of the orbital profile using the Wilson--Devinney code suggests that 2MASS J11201034-2201340 is a short-period A-type contact binary and the more massive component has a cool spot. The X-ray emission was first noted in observations made by \swift\, then further confirmed and characterized by an \xmm\ observation. The X-ray spectrum can be described by a power law or thermal Bremsstrahlung. Unfortunately, we could not observe significant X-ray orbital modulation. Finally, according to the spectral energy distribution, this system is estimated to be 690 pc from Earth with a calculated X-ray intensity of $(0.7-1.5)\times 10^{30}$ erg s$^{-1}$, which is in the expected range of an X-ray emitting contact binary.