  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 TESS mission. We extracted, analysed, and modelled the light curves of
$\sim 90000$ 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--$R_{\rm P}$
distribution of candidate and confirmed exoplanets with periods $<100$ days and
well constrained ages. While no peculiar trends are observed for Jupiter-size
and (super-)Earth-size planets, we found that objects with $4\,R_{\rm Earth}
\lesssim R_{\rm P} \lesssim 13\,R_{\rm Earth}$ are concentrated at ages
$\lesssim 200$ Myr; different scenarios (atmospheric losses, migration, etc.)
are considered to explain the observed age-$R_{\rm P}$ distribution.
