In a previous paper, we reported evidence for quasi-periodicities in the \textsl{TESS} light curves of BL Lacerate and two other blazars found serendipitously in the SDSS AGN catalog. In this work, we find tentative evidence for quasi-periodic features in the \textsl{TESS} observations of five sources in the fourth catalog of the Fermi--LAT (4FGL) sources: J090453.4$-$573503, J2345$-$1555, B0422+004, J002159.2$-$514028, and B0537$-$441. We analysed the \textsl{TESS} light curves of these blazars that we extracted using a customized approach. The quasi-periodic oscillations (QPOs) are searched for using two timing analysis techniques: generalized Lomb-Scargle periodogram and weighted wavelet Z-transform. Their apparent periods lie in the range of 2.8--6.5 days and have at least 3$\sigma$ significance in both of these methods. QPOs at such timescales can originate from the kink instability model which relates the quasi-periodic feature with the growth of kinks in the magnetized relativistic jets. We performed MCMC simulations to obtain the posterior distribution of parameters associated with this model and found the kink period consistent with previous studies.
Comment: 12 pages, 4 figures. Accepted for publication in MNRAS main journal