  Given their extremely large distances and small apparent sizes, quasars are
generally considered as objects with near-zero parallax and proper motion.
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.
These quasars may come with astrometric jitter detectable with Gaia data, or
significant changes in the position at different wavelengths. 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. We propose a series of criteria for selecting
abnormal quasars based on Gaia astrometric data. We obtain two catalogs
containing 155 sources and 44 sources, respectively. They are potential
candidates of quasar pairs.
