ABSTRACT The knowledge of the ages of stars hosting exoplanets allows us to obtain an overview on the evolution of exoplanets and understand the mechanisms affecting their life. The measurement of the ages of stars in the Galaxy is usually affected by large uncertainties. An exception are the stellar clusters: For their coeval members, born from the same molecular cloud, ages can be measured with extreme accuracy. In this context, the project PATHOS is providing candidate exoplanets orbiting members of stellar clusters and associations through the analysis of high-precision light curves obtained with cutting-edge tools. In this work, we exploited the data collected during the second year of the Transiting Exoplanet Survey Satellite mission. We extracted, analysed, and modelled the light curves of $\sim 90\, 000$ stars in open clusters located in the Northern ecliptic hemisphere in order to find candidate exoplanets. We measured the frequencies of candidate exoplanets in open clusters for different orbital periods and planetary radii, taking into account the detection efficiency of our pipeline and the false positive probabilities of our candidates. We analysed the age–RP distribution of candidate and confirmed exoplanets with periods <100 d and well constrained ages. While no peculiar trends are observed for Jupiter-size and (super-)Earth-size planets, we found that objects with $4 \lesssim R_{\rm P} \lesssim 13R_{\rm Earth}$ are concentrated at ages ≲200 Myr; different scenarios (atmospheric losses, migration, etc.) are considered to explain the observed age–RP distribution.