  In the manuscript, a candidate of sub-pc binary black hole (BBH) system is
reported in SDSS J1257+2023 through different properties of broad Balmer
emission lines. After subtractions of host galaxy contributions, Gaussian
functions are applied to measure emission lines in SDSS J1257+2023, leading
line width (second moment) 760${\rm km/s}$ of broad H$\beta$ to be 0.69 times
of line width 1100${\rm km/s}$ of broad H$\alpha$, quite different from normal
line width ratio 1.1 of broad H$\beta$ to broad H$\alpha$ in quasars. The quite
broader component in broad H$\alpha$ in SDSS J1257+2023 can be confirmed with
confidence level higher than $5\sigma$ through F-test technique, through
different model functions applied to measure emission lines. The broad Balmer
emission lines having different line widths can be naturally explained by a BBH
system with different obscurations on central two independent BLRs. Meanwhile,
through ZTF light curves and corresponding phase folded light curves well
described by sinusoidal function, BBH system expected optical QPOs can be
detected with periodicity about 1000days, confirmed with confidence level
higher than $3\sigma$ by Generalized Lomb-Scargle periodogram. And through CAR
process simulated light curves, confidence level higher than $2\sigma$ can be
determined to support the optical QPOs in SDSS J1257+2023 not from intrinsic
AGN activities, although the ZTF light curves have short time durations.
Moreover, through oversimplified BBH system simulated results, studying
different broad Balmer lines as signs of BBH systems in normal quasars with
flux ratios around 4 of broad H$\alpha$ to broad H$\beta$ could be done in near
future.
