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Galactic sites of acceleration of cosmic rays to energies of order 10^15 eV and higher, dubbed PeVatrons, reveal themselves by recently discovered gamma radiation of energies above 100 TeV. However, joint gamma-ray and neutrino production, which marks unambiguously cosmic-ray interactions with ambient matter and radiation, was not observed until now. In November 2020, the IceCube neutrino observatory reported an ~150 TeV neutrino event from the direction of one of the most promising Galactic PeVatrons, the Cygnus Cocoon. Here we report on the observation of a 3.1-sigma (post trial) excess of atmospheric air showers from the same direction, observed by the Carpet-2 experiment and consistent with a few-months flare in photons above 300 TeV, in temporal coincidence with the neutrino event. The fluence of the gamma-ray flare is of the same order as that expected from the neutrino observation, assuming the standard mechanism of neutrino production. This is the first evidence for the joint production of high-energy neutrinos and gamma rays in a Galactic source., 7 pages, 3 figures, AASTeX. V2: minor changes; Appendix with more analysis details added. Version accepted by Astrophys. J. Letters. V3: title corrected (text unchanged), matches the published version