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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 X-3 at X-ray and radio ranges is found. Gamma-ray spectra in the whole range up to 100 TeV, including flaring, quenching states, as well as the phase-resolved one are obtained. Also, Cyg X-3 was established as a MeV-GeV γ-ray source in Fermi LAT observations, starting in 2008. Very recently, the detection of variable multi-TeV emission from Cyg X-3 by SHALON was confirmed in observations by LHAASO. Moreover, the extension of the SHALON-measured spectrum of Cyg X-3 up to 3.5 PeV was obtained. These detections of orbital-modulated emission in the range from MeV through TeV and up to PeV energies, which also connected with flaring activity of Cyg X-3, point to the generation of gamma-rays in the innermost region of the relativistic jet, ejected from the central regions around the black hole, which is evidence of the efficient acceleration of the cosmic rays up to the 10 17 eV in this galactic binary.