We report the identification of 64 new candidates of compact galaxies, potentially hosting faint quasars with bolometric luminosities of Lbol=10^43^-10^46^erg/s, residing in the reionization epoch within the redshift range of 6<~z<~8. These candidates were selected by harnessing the rich multiband datasets provided by the emerging JWST-driven extragalactic surveys, focusing on COSMOS-Web, as well as JADES, UNCOVER, CEERS, and PRIMER. Our search strategy includes two stages: applying stringent photometric cuts to catalog-level data and detailed spectral energy distribution fitting. These techniques effectively isolate the quasar candidates while mitigating contamination from low-redshift interlopers, such as brown dwarfs and nearby galaxies. The selected candidates indicate physical traits compatible with low-luminosity active galactic nuclei, likely hosting ~10^5^-10^7^M_{sun}_ supermassive black holes (SMBHs) living in galaxies with stellar masses of ~10^8^-10^10^M_{sun}_. The SMBHs selected in this study, on average, exhibit an elevated mass compared to their hosts, with the mass ratio distribution slightly higher than those of galaxies in the local Universe. As with other high-z studies, this is at least in part due to the selection method for these quasars. An extensive Monte Carlo analysis provides compelling evidence that heavy black hole seeds from the direct collapse scenario appear to be the preferred pathway to mature this specific subset of SMBHs by z~7. Notably, most of the selected candidates might have emerged from seeds with masses of ~10^5^M_{sun}_, assuming a thin disk accretion with an average Eddington ratio of f_Edd_=0.6+/-0.3 and a radiative efficiency of epsilon=0.2+/-0.1. This work underscores the significance of further spectroscopic observations, as the quasar candidates presented here offer exceptional opportunities to delve into the nature of the earliest galaxies and SMBHs that formed during cosmic infancy.