A Bayesian mixture modeling method was applied to Chandra Deep Field South (CDF‐S) to find faint extended sources at high redshift.The probabilistic two‐component mixture model allows the separation of the diffuse background from celestial sources within a one‐step algorithm without data censoring. The background is modeled with a thin‐plate spline.The source and background estimation method was extended to allow the flux of celestial objects to be inverse‐Gamma distributed. In addition, all the detected sources are automatically parameterized to produce a list of source positions, count rates and morphological parameters.The present analysis is applied to the CDF‐S. With its 940 ksec of exposure time, CDF‐S is one of the deepest X‐ray observations performed. We analyze the 0.5–2 keV energy band to search for clusters or groups of galaxies. Point‐like and extended sources are separated incorporating the knowledge of the observatory’s point spread function (PSF).Combining the Bayesian mixture modeling tech...