Selection criteria for extended sources. The selection is performed in the extension likelihood - extent plane. The red-solid lines define the optimal parameters obtained from simulations to characterize extended sources. Left: simulation results. Gray dots represent simulated AGNs, and blue triangles, false detections. Colored stars represent clusters with different input fluxes. Right: results from reprocessing RASS data. Gray dots stand for point-like detections and the star symbols for the cluster candidates. Green and pink stars show the candidates with identified counterparts in the MCXC and PSZ2 catalogs, respectively. The black stars represent the 13 groups of our pilot sample described in Table 3.