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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 Hβ line from the broad line region, we obtain an estimate of the black hole mass MBH, Hβ ∼ 2.7 × 109 M⊙. This value is within a factor ≲1.5 of the Hα-based black hole mass from the same spectrum (MBH, Hα ∼ 1.93 × 109 M⊙) and is consistent with a previous estimate relying on the Mg IIλ2799 line (MBH, MgII ∼ 2.65 × 109 M⊙). All these MBH estimates are within the ∼0.5 dex intrinsic scatter of the adopted mass calibrations. The high Eddington ratio of PJ308-21 λEdd, Hβ ∼ 0.67 (λEdd, Hα ∼ 0.96) is in line with the overall quasar population at z ≳ 6. The relative strengths of the [O III], Fe II, and Hβ lines are consistent with the empirical "Eigenvector 1" correlations as observed for low redshift quasars. We find evidence for blueshifted [O III] λ5007 emission with a velocity offset Δv[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 Δv[O III] and FWHM([O III]) likely being more uncertain due to the blending with Hβ 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. [ABSTRACT FROM AUTHOR]