The properties of quasar-host galaxies might be determined by the growth and feedback of their supermassive (SMBH, 10 8−10 M ) black holes. We investigate such connection with a suite of cosmological simulations of massive (halo mass ≈ 10 12 M ) galaxies at 𝑧 6 which include a detailed sub-grid multiphase gas and accretion model. BH seeds of initial mass 10 5 M grow mostly by gas accretion, and become SMBH by 𝑧 = 6 setting on the observed 𝑀 BH − 𝑀 ★ relation without the need for a boost factor. Although quasar feedback crucially controls the SMBH growth, its impact on the properties of the host galaxy at 𝑧 = 6 is negligible. In our model, quasar activity can both quench (via gas heating) or enhance (by ISM over-pressurization) star formation. However, we find that the star formation history is insensitive to such modulation as it is largely dominated, at least at 𝑧 > 6, by cold gas accretion from the environment that cannot be hindered by the quasar energy deposition. Although quasar-driven outflows can achieve velocities > 1000 km s −1 , only ≈ 4% of the outflowing gas mass can actually escape from the host galaxy. These findings are only loosely constrained by available data, but can guide observational campaigns searching for signatures of quasar feedback in early galaxies.