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We present spectroscopic confirmation of three new two-image gravitationally lensed quasars, compiled from existing strong lens and X-ray catalogs. Images of HSC J091843.27$-$022007.5 show a red galaxy with two blue point sources at either side, separated by 2.26 arcsec. This system has a source and a lens redshifts $z_s=0.804$ and $z_{\ell}=0.459$, respectively, as obtained by our follow-up spectroscopic data. CXCO J100201.50$+$020330.0 shows two point sources separated by 0.85 arcsec on either side of an early-type galaxy. The follow-up spectroscopic data confirm the fainter quasar has the same redshift with the brighter quasar from the SDSS fiber spectrum at $z_s=2.016$. The deflecting foreground galaxy is a typical early-type galaxy at a redshift of $z_{\ell}=0.439$. SDSS J135944.21$+$012809.8 has two point sources with quasar spectra at the same redshift $z_s=1.096$, separated by 1.05 arcsec, and fits to the HSC images confirm the presence of a galaxy between these. These discoveries demonstrate the power of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP)'s deep imaging and wide sky coverage. Combined with existing X-ray source catalogues and follow-up spectroscopy, the HSC-SSP provides us unique opportunities to find multiple-image quasars lensed by a foreground galaxy.