  We present a systematic search for periodically varying quasar and
supermassive black hole binary (SMBHB) candidates in the Pan-STARRS1 Medium
Deep Survey. From $\sim9,000$ color-selected quasars in a $\sim50$ deg$^{2}$
sky area, we initially identify $26$ candidates with more than $1.5$ cycles of
variation. We extend the baseline of observations via our imaging campaign with
the Discovery Channel Telescope and the Las Cumbres Observatory network and
reevaluate the candidates using a more rigorous, maximum likelihood method.
Using a range of statistical criteria and assuming the Damped Random Walk model
for normal quasar variability, we identify one statistically significant
periodic candidate. We also investigate the capabilities of detecting SMBHBs by
the Large Synoptic Survey Telescope using our study with MDS as a benchmark and
explore any complementary, multiwavelength evidence for SMBHBs in our sample.
