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We report the discovery of new lensed quasar candidates in the imaging dataof the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) DR4, covering$1\,310~{\rm deg}^2$ of the sky with seeing of $\approx0.6''$. In addition totwo catalogs of MILLIQUAS and AllWISEAGN, which contain confirmed and candidatequasars, we preselect quasar sources using color cuts from the HSC ($grizy$)and unWISE ($W1+W2$) photometric data based on SDSS spectroscopic catalogs. Wesearch for the presence of multiple point sources with similar color throughthe convolution of the Laplacian of the preselected quasar image cutouts withthe Laplacian of the point spread function, resulting in a reduction of lenscandidates from $1\,652\,329$ to $121\,511$ ($7.4\%$). After visual binaryclassification, we grade $6\,199$ ($0.4\%$) potential lenses on a scale of 0 to3, with 3 indicating a lens and 0 indicating a non-lens. Finally we obtain 162lens candidates with an average grade of $\geq2$, and among them, wesuccessfully recover 18 known lenses. By fitting the light distribution andremoving the known contaminants, we discover that 57 new systems contain atleast two point sources and a galaxy in between, including 10 possiblequadruply lensed quasars. This new sample of lens candidates exhibits a medianseparation of $1.26''$ and a magnitude limit of $i\approx22$. Spectroscopic orhigh-resolution imaging follow up on these newly discovered lensed quasarcandidates will further allow their natures to be confirmed.

Survey of Gravitationally Lensed Objects in HSC Imaging (SuGOHI). IX. Discovery of Strongly Lensed Quasar Candidates