With the superb angular resolution of the Chandra Observatory, it is now possible to detect X-ray point sources, either embedded in galaxy clusters or along the cluster line of sight, which could not be resolved by previous instruments. This now allows studies of source counts in distant cluster fields. A sample of 18 distant (0.25 < z < 1.01) galaxy clusters from the Chandra archive were used to analyze the inner region of clusters of galaxies to check for the presence of any overdensity of X-ray point sources embedded in the gas diffuse emission. We constructed the logN-logS, in both the soft and hard energy bands, for the X-ray point sources detected in the central cluster region (within 1 Mpc)to be compared with the counts of point sources detected in similarly deep fields without clusters. We find a ~ 2 sigma excess of cluster region sources at the bright end of the logN-logS. The radial distribution of the brightest X-ray point sources confirms this excess and indicates that it is confined to the inner 0.5 Mpc of the cluster region. The results suggest the possible existence of X-ray sources belonging to the cluster (most probably AGN, given their 0.5-10 keV luminosity ranging from 10^43 to 10^44 erg/s): on average one every three clusters. The X-ray source excess found here is much smaller than the excess of radio galaxies found recently in high-z X-ray selected clusters, possibly due to the higher sensitivity of the radio observations.
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