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Context.We identified and analysed massive quiescent galaxies (MQGs) atz ≈ 3.1 within the 2 deg²COSMOS field and explored the effect of the galaxy environment on quenching processes. By examining the variation in the quenched fraction and physical properties of these galaxies in different environmental contexts, including local densities, protoclusters, and cosmic filaments, we investigated the connection between environmental factors and galaxy quenching at cosmic noon. Aims.We selected MQGs atz ≈ 3.1 using deep photometric data from the COSMOS2020 catalogue combined with narrow-band-selected Lyman-αemitters (LAEs) from the One-hundred-square-degree DECam Imaging in Narrowbands (ODIN) survey. We performed a spectral energy distribution fitting using the code BAGPIPES to derive the star formation histories and quenching timescales. We constructed Voronoi-tessellation density maps using LAEs, and we independently selected galaxies photometrically to characterize the galaxy environments. Methods.We identified 24 MQGs atz ≈ 3.1, each of which has a stellar mass higher than 10^10.6 M_⊙. These MQGs share remarkably uniform star-formation histories, with intense starburst phases followed by rapid quenching within short timescales (≤400 Myr). The consistency of these quenching timescales suggests a universal and highly efficient quenching mechanism in this epoch. We found no significant correlation between environmental density (either local or large scale) and galaxy quenching parameters such as the quenching duration, the quenched fraction, or the timing. MQGs show no preferential distribution with respect to protoclusters or filaments compared to massive star-forming galaxies. Some MQGs reside close to gas-rich filaments, but show no evidence of rejuvenated star formation. This implies gas-heating mechanisms and not gas exhaustion. These results indicate that the quenching processes atz ≈ 3.1 likely depend little on the immediate galaxy environment. Results.Our findings suggest that environmental processes alone, such as galaxy mergers, interactions, or gas stripping, cannot fully explain the galaxy quenching atz ≈ 3.1. Internal mechanisms such as feedback from AGN, stellar feedback, virial shock heating, or morphological quenching instead play an important role in quenching. Future spectroscopic observations must confirm the quiescent nature and precise redshifts of these galaxies. Observational studies of gas dynamics, gas temperature, and ionisation conditions within and around MQGs will also clarify the physical mechanisms driving galaxy quenching during this critical epoch of galaxy evolution.