Since the discovery of the first quasar in 1963 ( Schmidt, 1963), this type of extremely distant active galactic nuclei (AGN) has gradually become the focus of astronomical research. They are potential candidates of quasar pairs. We obtain two catalogs containing 155 sources and 44 sources, respectively. We propose a series of criteria for selecting abnormal quasars based on Gaia astrometric data. In this work, we aim to find these quasar candidates from Gaia EDR3 astrometric data combining with Sloan Digital Sky Survey (SDSS) spectroscopic data to provide a candidate catalog to the science community. These quasars may come with astrometric jitter detectable with Gaia data, or significant changes in the position at different wavelengths. However, some special quasars may have abnormal astrometric characteristics, such as quasar pairs, lensed quasars, AGNs with bright parsec-scale optical jets, which are scientifically interesting objects, such as binary black holes. Given their extremely large distances and small apparent sizes, quasars are generally considered as objects with near-zero parallax and proper motion.
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