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. We want to analyze the inner region of clusters of galaxies to check for the presence of any over-density of X-ray point sources embedded in the gas diffuse emission. These point sources are possible AGN belonging to the clusters and could contaminate the cluster emission. We used a sample of 18 distant (0.25<z<1.01) galaxy clusters from the Chandra archive to construct the logN-logS, in both the soft and hard energy bands, for the X-ray point sources detected in the central cluster region to be compared with the counts of point sources detected in similarly deep fields without clusters.