  There are some strange quasars with multiple Gaia detections or observed with
abnormal astrometric characteristics, such as with large proper motions or
significant astrometric noises. Those strange quasars could be potential
candidates of quasar-star pairs, dual quasars (DQs), or lensed quasars (LQs).
Searching for both DQs and LQs is of great importance in many fields of
astrophysics. Here in this work, we select 143 SDSS spectroscopically confirmed
quasars that have multiple Gaia EDR3 detections within 1 arcsec of the SDSS
quasar' position. We apply several optical identification methods to classify
this sample. We firstly exclude 65 quasar-star pairs via their stellar features
including their parallaxes and proper motions, stellar features in the SDSS
spectra, or via the colour-colour diagram. Based on the spectral-fitting
results, we find 2 DQ candidates, one of which presents a double-peaked [O III]
emission line feature and the other shows a broad $H_{\beta}$ velocity offset
($\sim$ 870 $ km s^{-1} $) relative to the [O III] $\lambda$5007 line. Via the
colour difference method, we further find 56 LQ candidates with similar colours
in their multiple images. We also cross-match 143 objects with the HST archive
and find 19 targets with archival HST images. Our classification results of
those 19 targets are mainly consistent with previous works.
