  Gaia's readout window strategy is challenged by very dense fields in the sky.
Therefore, in addition to standard Gaia observations, full Sky Mapper (SM)
images were recorded for nine selected regions in the sky. A new software
pipeline exploits these Service Interface Function (SIF) images of crowded
fields (CFs), making use of the availability of the full two-dimensional (2D)
information. This new pipeline produced half a million additional Gaia sources
in the region of the omega Centauri ($\omega$ Cen) cluster, which are published
with this Focused Product Release. We discuss the dedicated SIF CF data
reduction pipeline, validate its data products, and introduce their Gaia
archive table. Our aim is to improve the completeness of the {\it Gaia} source
inventory in a very dense region in the sky, $\omega$ Cen. An adapted version
of {\it Gaia}'s Source Detection and Image Parameter Determination software
located sources in the 2D SIF CF images. We validated the results by comparing
them to the public {\it Gaia} DR3 catalogue and external Hubble Space Telescope
data. With this Focused Product Release, 526\,587 new sources have been added
to the {\it Gaia} catalogue in $\omega$ Cen. Apart from positions and
brightnesses, the additional catalogue contains parallaxes and proper motions,
but no meaningful colour information. While SIF CF source parameters generally
have a lower precision than nominal {\it Gaia} sources, in the cluster centre
they increase the depth of the combined catalogue by three magnitudes and
improve the source density by a factor of ten. This first SIF CF data
publication already adds great value to the {\it Gaia} catalogue. It
demonstrates what to expect for the fourth {\it Gaia} catalogue, which will
contain additional sources for all nine SIF CF regions.
