  We report the identification of 64 new candidates of compact galaxies,
potentially hosting faint quasars with bolometric luminosities of
$L_\mathrm{bol} = 10^{43}$--10$^{46}$ erg s$^{-1}$, residing in the
reionization epoch within the redshift range of $6 \lesssim z \lesssim 8$.
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 $\approx10^5$--$10^7~M_\odot$ supermassive black holes (SMBHs)
living in galaxies with stellar masses of $\approx10^8$--$10^{10}~M_\odot$. 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 $z\approx7$. 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.
