We present a systematic search for periodically varying quasars and supermassive black hole binary (SMBHB) candidates in the Pan-STARRS1 (PS1) Medium Deep Surveys MD09 field. From a color-selected sample of 670 quasars extracted from a multi-band deep-stack catalog of point sources, we locally select variable quasars and look for coherent periods with the Lomb-Scargle periodogram. Three candidates from our sample demonstrate strong variability for more than ~3 cycles, and their PS1 light curves are well fitted to sinusoidal functions. We test the persistence of the candidates apparent periodic variations detected during the 4.2 years of the PS1 survey with archival photometric data from the SDSS Stripe 82 survey or new monitoring with the Large Monolithic Imager at the Discovery Channel Telescope. None of the three periodic candidates (including PSO J334.2028+1.4075) remain persistent over the extended baseline of 7 - 14 years, corresponding to a detection rate of < 1 in 670 quasars in a search area of 5 deg^2. Even though SMBHBs should be a common product of the hierarchal growth of galaxies, and periodic variability in SMBHBs has been theoretically predicted, a systematic search for such signatures in a large optical survey is strongly limited by its temporal baseline and the red noise associated with normal quasar variability. We show that follow-up long-term monitoring (>5 cycles) is crucial to our search for these systems.
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