Context. 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 (ω 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. Aims. Our aim is to improve the completeness of the Gaia source inventory in a very dense region in the sky, ω Cen. Methods. An adapted version of Gaia's Source Detection and Image Parameter Determination software located sources in the 2D SIF CF images. These source detections were clustered and assigned to new SIF CF or existing Gaia sources by Gaia s cross-match software. For the new sources, astrometry was calculated using the Astrometric Global Iterative Solution software, and photometry was obtained in the Gaia DR3 reference system. We validated the results by comparing them to the public Gaia DR3 catalogue and external Hubble Space Telescope data. Results. With this Focused Product Release, 526 587 new sources have been added to the Gaia catalogue in ω 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 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. Conclusions. This first SIF CF data publication already adds great value to the Gaia catalogue. It demonstrates what to expect for the fourth Gaia catalogue, which will contain additional sources for all nine SIF CF regions.