  We present a first statistical sample of faint type-1 AGNs at $z>4$
identified by JWST/NIRSpec deep spectroscopy. Among the 185 galaxies at
$z_\mathrm{spec}=3.8-8.9$ confirmed with NIRSpec, our systematic search for
broad-line emission reveals 10 type-1 AGNs at $z=4.015-6.936$ whose broad
component is only seen in the permitted H$\alpha$ line and not in the forbidden
[OIII]$\lambda$5007 line that is detected with greater significance than
H$\alpha$. The broad H$\alpha$ line widths of $\mathrm{FWHM}\simeq1000-6000\
\mathrm{km\ s^{-1}}$ suggest that the AGNs have low-mass black holes with
$M_\mathrm{BH}\sim10^6-10^8\ M_\odot$, remarkably lower than those of
low-luminosity quasars previously identified at $z>4$ with ground-based
telescopes. JWST and HST high-resolution images reveal that the majority of
them show extended morphologies indicating significant contribution to the
total lights from their host galaxies, except for three compact objects two of
which show red SEDs, probably in a transition phase from faint AGNs to low
luminosity quasars. Careful AGN-host decomposition analyses show that their
host's stellar masses are systematically lower than the local relation between
the black hole mass and the stellar mass, implying a fast black hole growth
consistent with predictions from theoretical simulations. A high fraction of
the broad-line AGNs ($\sim5\%$), higher than $z\sim0$, indicates that a number
density of such faint AGNs is higher than an extrapolation of the quasar
luminosity function, implying a large population of AGNs including type 1 and
type 2 in the early universe. Such faint AGNs contribute to cosmic
reionization, while the total contribution is not large, up to $\sim50\%$ at
$z\sim6$, because of their faint nature.
