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ABSTRACT Negative feedback from accreting supermassive black holes is considered crucial in suppressing star formation and quenching massive galaxies. However, several models and observations suggest that black hole feedback may have a positive effect, triggering star formation by compressing interstellar medium gas to higher densities. We investigate the dual role of black hole feedback using cosmological hydrodynamic simulations from the Feedback In Realistic Environment (FIRE) project, incorporating a novel implementation of hyper-refined accretion-disc winds. Focusing on a massive, star-forming galaxy at z ∼ 2 ($$M_{\rm halo} \sim 10^{12.5}\, {\rm M}_{\odot }$$), we demonstrate that strong quasar winds with a kinetic power of ∼1046 erg s−1, persisting for over 20 Myr, drive the formation of a central gas cavity and significantly reduce the surface density of star formation across the galaxy’s disc. The suppression of star formation primarily occurs by limiting the availability of gas for star formation rather than by evacuating the pre-existing star-forming gas reservoir (preventive feedback dominates over ejective feedback). Despite the overall negative impact of quasar winds, we identify several potential indicators of local positive feedback, including (1) the spatial anticorrelation between wind-dominated regions and star-forming clumps, (2) higher local star formation efficiency in compressed gas at the edge of the cavity, and (3) increased contribution of outflowing material to local star formation. Moreover, stars formed under the influence of quasar winds tend to be located at larger radial distances. Our findings suggest that both positive and negative AGN feedback can coexist within galaxies, although the local positive triggering of star formation has a minor influence on global galaxy growth.