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 μm wavelength range and shows the rest-frame optical emission of the quasar with exquisite quality (signal-to-noise ratio ∼100 − 400 per spectral element). Based on the H β line from the broad line region, we obtain an estimate of the black hole mass M _{BH, H β}  ∼ 2.7 × 10 ⁹   M _⊙ . This value is within a factor ≲1.5 of the H α -based black hole mass from the same spectrum ( M _{BH, H α}  ∼ 1.93 × 10 ⁹   M _⊙ ) and is consistent with a previous estimate relying on the Mg  II λ 2799 line ( M _BH, MgII  ∼ 2.65 × 10 ⁹   M _⊙ ). All these M _BH estimates are within the ∼0.5 dex intrinsic scatter of the adopted mass calibrations. The high Eddington ratio of PJ308-21 λ _{Edd, H β}  ∼ 0.67 ( λ _{Edd, H α}  ∼ 0.96) is in line with the overall quasar population at z  ≳ 6. The relative strengths of the [O  III ], Fe  II , and H β lines are consistent with the empirical “Eigenvector 1” correlations as observed for low redshift quasars. We find evidence for blueshifted [O  III ] λ 5007 emission with a velocity offset Δ v _{[O III]}  = −1922 ± 39 km s ⁻¹ from the systemic velocity and a full width at half maximum (FWHM) FWHM ([O  III ]) = 2776 ₋₇₄ ⁺⁷⁵ km s ⁻¹ . This may be the signature of outflowing gas from the nuclear region, despite the true values of Δ v _{[O III]} and FWHM ([O  III ]) likely being more uncertain due to the blending with H β and Fe  II lines. Our study demonstrates the unique capabilities of NIRSpec in capturing quasar spectra at cosmic dawn and studying their properties in unprecedented detail.