Title: A candidate period of 4.605 day for FRB 20121102A and one possible implication of its origin

Abstract: A firm establishment of the presence or the lack of periodicity in repeating Fast Radio Bursts (FRBs) is crucial for determining their origins. Here we compile 1145 radio bursts of FRB 20121102A with fluence larger than 0.15 Jy ms from observations using the Five-hundredmeter Aperture Spherical radio Telescope, Arecibo Observatory, Green Bank Telescope, Effelsberg Telescope, MeerKAT Telescope, Lovell Telescope, Deep Space Network 70 m radio telescopes, Very Large Array, and the Westerbork Synthesis Radio Telescope spanning the time interval of MJD 57175-58776. A quasi-period of $157.1_{-4.8}^{+5.2}$ day and a candidate quasi-period of $4.605_{-0.010}^{+0.003}$ day are found through the phase-folding probability binomial analysis. The former is consistent with previous findings and the latter is new. The 4.605 day periodicity is more obvious in high-energy bursts with fluence larger than $10^{38}$ erg. The presence of these (candidate) quasi-periods, together with the corresponding width of burst accumulation in the phase space, are consistent with the bursts' originating from a binary degenerate star system with a close-by planet around the primary neutron star.