The $\gamma$-ray blazar PKS 0903-57 had strong flaring episodes in high energy (HE;~100~MeV~$\leq$~E~$\leq$~100~GeV) and very high-energy (VHE; 100 GeV $\leq$ E $\leq$ 10 TeV) gamma rays in 2020 through 2022. The presence of a nearby star has posed a challenge over the years to efforts aimed at characterizing the nature of the blazar. The star is located at a distance of 0.67" from PKS 0903-57, essentially resulting in somewhat an obscuration of the blazar from observers. During the flaring period, the optical counterpart of PKS 0903-57 underwent spectroscopic observations by the Southern African Large Telescope (SALT) and the Very Large Telescope (VLT). Photometric monitoring was also performed with the Rapid Eye Mount (REM) telescope. Using recent (2024) VLT observations taken with a narrower slit (0.5" wide) under subarcsecond seeing ($\sim$0.5") conditions enabled the isolation of the signatures of the blazar from those of the star. This resulted in a firm measurement of the blazar's redshift $z$ = 0.2621 ± 0.0006, using five narrow emission lines detected in the spectra. Additionally, a symmetric broad H$\alpha$ line with full width at half maximum of 4020 $\pm$ 30 km/s was also detected. The spectrum revealed a jet-dominated continuum, which led to classifying PKS 0903-57 as a flat-spectrum radio quasar. Moreover, a redshift offset ($\sim$1500 km/s) between the broad H$\alpha$ line and its narrow line counterpart, was detected with high significance. When compared to findings in the literature of similar systems, the detection implies several possibilities, including an unusual accretion mechanism, a merging of two supermassive black holes, or an ejection of a merged black hole from the system.