  We conduct a systematic search for quasars with periodic variations from the
archival photometric data of the Zwicky Transient Facility by cross-matching
with the quasar catalogs of the Sloan Digital Sky Survey and V{\'e}ron-Cetty \&
V{\'e}ron. We first select out 184 primitive periodic candidates using the
generalized Lomb-Scargle periodogram and auto-correlation function and then
estimate their statistical significance of periodicity based on two red-noise
models, i.e., damped random walk (DRW) and single power-law (SPL) models. As
such, we finally identify 106 (DRW) and 86 (SPL) candidates with the most
significant periodic variations out of 143,700 quasars. We further compare DRW
and SPL models using Bayes factors, which indicate a relative preference of the
SPL model for our primitive sample. We thus adopt the candidates identified
with SPL as the final sample and summarize its basic properties. We extend the
light curves of the selected candidates by supplying other archival survey data
to verify their periodicity. However, only three candidates (with 6-8 cycles of
periods) meet the selection criteria. This result clearly implies that, instead
of being strictly periodic, the variability must be quasi-periodic or caused by
stochastic red-noise. This exerts a challenge to the existing search approaches
and calls for developing new effective methods.
