  Context. Strongly lensed quasars are fundamental sources for cosmology. The
Gaia space mission covers the entire sky with the unprecedented resolution of
$0.18$" in the optical, making it an ideal instrument to search for
gravitational lenses down to the limiting magnitude of 21. Nevertheless, the
previous Gaia Data Releases are known to be incomplete for small angular
separations such as those expected for most lenses. Aims. We present the Data
Processing and Analysis Consortium GravLens pipeline, which was built to
analyse all Gaia detections around quasars and to cluster them into sources,
thus producing a catalogue of secondary sources around each quasar. We analysed
the resulting catalogue to produce scores that indicate source configurations
that are compatible with strongly lensed quasars. Methods. GravLens uses the
DBSCAN unsupervised clustering algorithm to detect sources around quasars. The
resulting catalogue of multiplets is then analysed with several methods to
identify potential gravitational lenses. We developed and applied an outlier
scoring method, a comparison between the average BP and RP spectra of the
components, and we also used an extremely randomised tree algorithm. These
methods produce scores to identify the most probable configurations and to
establish a list of lens candidates. Results. We analysed the environment of 3
760 032 quasars. A total of 4 760 920 sources, including the quasars, were
found within 6" of the quasar positions. This list is given in the Gaia
archive. In 87\% of cases, the quasar remains a single source, and in 501 385
cases neighbouring sources were detected. We propose a list of 381 lensed
candidates, of which we identified 49 as the most promising. Beyond these
candidates, the associate tables in this Focused Product Release allow the
entire community to explore the unique Gaia data for strong lensing studies
further.
