  We present JWST/NIRSpec integral field data of the quasar PJ308-21 at
$z=6.2342$. As shown by previous ALMA and HST imaging, the quasar has two
companion sources, interacting with the quasar host galaxy. The high-resolution
G395H/290LP NIRSpec spectrum covers the $2.87-5.27\ \rm \mu m$ wavelength range
and shows the rest-frame optical emission of the quasar with exquisite quality
($S/N\sim 100-400$ per spectral element). Based on the H$\beta$ line from the
broad line region, we obtain an estimate of the black hole mass $M_{\rm
BH,H\beta}\sim 2.7\times 10^{9}\ \rm M_{\odot}$. This value is within a factor
$\lesssim 1.5$ of the H$\alpha$-based black hole mass from the same spectrum
($M_{\rm BH, H\alpha}\sim 1.93\times 10^{9}\ \rm M_{\odot}$) and is consistent
with a previous estimate relying on the MgII $\lambda 2799$ ($M_{\rm BH,
MgII}\sim 2.65\times 10^{9}\ \rm M_{\odot}$). All these $M_{\rm BH}$ are within
the $\sim 0.5$ dex intrinsic scatter of the adopted mass calibrations. The high
Eddington ratio of PJ308-21 $\lambda_{\rm Edd,H\beta}\sim 0.67$ ($\lambda_{\rm
Edd,H\alpha}\sim 0.96$) is in line with the overall quasar population at $z
\gtrsim 6$. The relative strengths of the [OIII], FeII and H$\beta$ lines are
consistent with the empirical "Eigenvector 1" correlations as observed for low
redshift quasars. We find evidence for blueshifted [OIII] $\lambda 5007$
emission with a velocity offset $\Delta v_{\rm [OIII]}=-1922\pm 39$ km s$^{-1}$
from the systemic velocity and a $\rm FWHM([OIII])=2776^{+75}_{-74}$ km
s$^{-1}$. This may be the signature of an outflow from the nuclear region,
despite the true values of $\Delta v_{\rm [OIII]}$ and $\rm FWHM([OIII])$ are
likely more uncertain due to the blending with H$\beta$ and FeII lines. Our
study demonstrates the unique capabilities of NIRSpec in capturing quasar
spectra at cosmic dawn and studying their properties in unprecedented detail.
