We here apply a novel technique selecting quasar candidates purely as sources with zero proper motions in the Gaia data release 2 (DR2). We demonstrate that this approach is highly efficient toward high Galactic latitudes with < 25% contamination from stellar sources. Such a selection technique offers a very pure sample completeness, since all cosmological point sources are selected regardless of their intrinsic spectral properties within the limiting magnitude of Gaia. We carry out a pilot-study by defining a sample compiled by including all Gaia-DR2 sources within one degree of the North Galactic Pole (NGP) selected to have proper motions consistent with zero within 2-sigma uncertainty. By cross-matching the sample to the optical Sloan Digital Sky Survey (SDSS) and the mid-infrared AllWISE photometric catalogues we investigate the colours of each of our sources. Together with already spectroscopically confirmed quasars we are therefore able to determine the efficiency of our selection. The majority of the zero proper motion sources have optical to mid-infrared colours consistent with known quasars. The remaining population may be contaminating stellar sources, but some may also be quasars with colours similar to stars. Spectroscopic follow-up of the zero proper motion sources is needed to unveil such a hitherto hidden quasar population. This approach has the potential to allow substantial progress on many important questions concerning quasars such as determining the fraction of dust-obscured quasars, the fraction of broad absorption line (BAL) quasars, and the metallicity distribution of damped Lyman-$alpha$ absorbers. The technique could also potentially reveal new types of quasars or even new classes of cosmological point sources.
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