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In the third paper of this series aimed at developing the tools for analysingresolved stellar populations using the cameras on board of the James Webb SpaceTelescope (JWST), we present a detailed multi-band study of the 2 Gyr Galacticopen cluster NGC 2506. We employ public calibration data-sets collected inmultiple filters to: (i) derive improved effective Point Spread Functions(ePSFs) for ten NIRCam filters; (ii) extract high-precision photometry andastrometry for stars in the cluster, approaching the main-sequence (MS) lowermass of ~0.1 Msun; and (iii) take advantage of the synergy between JWST andGaia DR3 to perform a comprehensive analysis of the cluster's global and localproperties. We derived a MS binary fraction of ~57.5 %, extending the Gaialimit (~0.8 Msun) to lower masses (~0.4 Msun) with JWST. We conducted a studyon the mass functions (MFs) of NGC 2506, mapping the mass segregation with Gaiadata, and extending MFs to lower masses with the JWST field. We also combinedinformation on the derived MFs to infer an estimate of the cluster present-daytotal mass. Lastly, we investigated the presence of white dwarfs (WDs) andidentified a strong candidate. However, to firmly establish its clustermembership, as well as that of four other WD candidates and of the majority offaint low-mass MS stars, further JWST equally deep observations will berequired. We make publicly available catalogues, atlases, and the improvedePSFs.

Photometry and astrometry with JWST -- III. A NIRCam-Gaia DR3 analysis of the open cluster NGC 2506