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Cyg X-3 is the famous galactic High-Mass X-ray binary system formed by a black hole that orbits a massive Wolf-Rayet star. Huge radio-flares are accompanied by the ejection of powerful jets like those seen in active galactic nuclei, making Cyg X-3 a microquasar-type object. Moreover, the activity of these jets is correlated with X-ray states. The X-ray and infrared emission from Cyg X-3 are modulated with a short period of 4.8-h which is supposed to be related to the emission scattering by the wind from the Wolf–Rayet companion star during the orbital motion of the compact object. Cyg X-3has long been considered to be a source of high and very high γ-ray, which would be evidence of the acceleration of the cosmic rays up to 10 17 eV. Gamma-ray emission in the energy range 800 GeV up to 100 TeV from Cyg X-3 was discovered by the SHALON telescope in 1995. The detected flux of gamma-rays up to 100 TeV is modulated with the orbital period of Cyg X-3 binary. During more than 20-year-long studies of Cyg X-3 at energies 800 GeV - 100 TeV by SHALON, the variable γ-ray emission corresponding to the different states for this object was detected. The correlation of TeV γ-ray flux increases with the flaring activity of Cyg