Abstract In this third paper of the series reporting on the reverberation mapping campaign of active galactic nuclei with asymmetric Hβ emission-line profiles, we present results for 15 Palomar–Green quasars using spectra obtained between the end of 2016–2021 May. This campaign combines long time spans with relatively high cadence. For eight objects, both the time lags obtained from the entire light curves and the measurements from individual observing seasons are provided. Reverberation mapping of nine of our targets has been attempted for the first time, while the results for six others can be compared with previous campaigns. We measure the Hβ time lags over periods of years and estimate their black hole masses. The long duration of the campaign enables us to investigate their broad-line region (BLR) geometry and kinematics for different years by using velocity-resolved lags, which demonstrate signatures of diverse BLR geometry and kinematics. The BLR geometry and kinematics of individual objects are discussed. In this sample, the BLR kinematics of Keplerian/virialized motion and inflow is more common than that of outflow.