A large number of quasars have also been identified through astrometry and mid-infrared methods (see, e.g., Secrest et al., 2015 Guo et al., 2018). There are many surveys concerning the identification of quasars such as the large Bright Quasar Survey ( Hewett et al., 1995), the 2DF Quasar Redshift Survey (2QZ, Croom et al., 2004), the quasars from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, Luo et al., 2012) and Solan Digital Sky Survey (SDSS, Pâris et al., 2018 Lyke et al., 2020). On the other hand, quasars are also a critical pathway to explore the evolution and mergers of galaxies in astrophysics ( Begelman et al., 1980 Shen et al., 2021). In astrometry, a large number of evenly distributed quasars can be used to establish a celestial reference frame ( Ma, 1997 Ma et al., 2009 Mignard et al., 2018 Charlot et al., 2020) because they have almost zero proper motions and point-like shapes. 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. 2School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing, China.1Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China.Qi-Qi Wu 1,2, Shi-Long Liao 1,2*, Xiang Ji 1,2, Zhao-Xiang Qi 1,2, Zhen-Ya Zheng 1,2, Ru-Qiu Lin 1,2, Ying-Kang Zhang 1,2 and Tao An 1,2
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