The origin of astrophysical neutrinos is one of the most debated topics today. Perhaps the most robust evidence of neutrino counterpart comes from supermassive black holes in active galactic nuclei associated with strongly collimated outflows, or jets, that can accelerate particles to relativistic energies and produce neutrinos through hadronic interactions. Similar outflows can also be found from X-ray binaries, or ‘microquasars’, that consist of a neutron star or a stellar-mass black hole accreting matter from a non-degenerate companion star. In some cases, these systems can accelerate particles up to GeV energies implying an efficient acceleration mechanism in their jets. Neutrino production in microquasar jets can be expected with suitable conditions and a hadronic particle population. Microquasar Cyg X-3 is a unique, short orbital period X-ray binary hosting a Wolf–Rayet companion star with a strong stellar wind. The interaction of the dense stellar wind with a relativistic jet leads to particle collisions followed by high-energy gamma-ray and potentially neutrino emission. Here, using the 10-yr neutrino candidate sample of the IceCube neutrino observatory, we find that the events with the highest spatial association with Cyg X-3 occur during short-lived high-energy gamma-ray flaring periods indicating the possible astrophysical nature of these events.