The James Webb Space Telescope will have the power to characterize high-redshift quasars at z > 6 with an unprecedented depth and spatial resolution. While the brightest quasars at such redshift (i.e., with bolometric luminosity Lbol > 10 erg/s) provide us with key information on the most extreme objects in the Universe, measuring the black hole (BH) mass and Eddington ratios of fainter quasars with Lbol = 10 −10 erg/s opens a path to understand the build-up of more normal BHs at z > 6. In this paper, we show that the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA large-scale cosmological simulations do not agree on whether BHs at z > 4 are overmassive or undermassive at fixed galaxy stellar mass with respect to the MBH −M? scaling relation at z = 0 (BH mass offsets). Our conclusions are unchanged when using the local scaling relation produced by each simulation or empirical relations. We find that the BH mass offsets of the simulated faint quasar population at z > 4, unlike those of bright quasars, represent the BH mass offsets of the entire BH population, for all the simulations. Thus, a population of faint quasars with Lbol = 10 45 − 10 erg/s observed by JWST can provide key constraints on the assembly of BHs at high redshift. Moreover, this will help constraining the highredshift regime of cosmological simulations, including BH seeding, early growth, and co-evolution with the host galaxies. Our results also motivate the need for simulations of larger cosmological volumes down to z ∼ 6, with the same diversity of sub-grid physics, in order to gain statistics on the most extreme objects at high redshift.