Based on observations supported by the Fast Radio Burst Major Project with the assistance of the five-hundred-meter aperture spherical radio telescope (FAST), we published a series of four papers on the more than 700 outbursts detected by the Repeating Fast Radio Burst (FRB) FRB 20201124A during an extremely active event on September 25-28, 2021. In these papers, the Burst Morphology, energy distribution, Polarimetry, and spin period search of FRB 20201124A during this active period were studied in detail. In the fourth paper of the series, we systematically searched for rotation periods and linear accelerations from 996 individual pulse-peak time series but no plausible rotation period was found. We also made a scrutiny into quasi-periodic multi-peak structure among them and concluded that we should be cautious to associate quasi-periodicity in the FRB multi-peak structure with the rotation of dense star at least for signals with significance below ∼ 4 σ,s.