  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.
