  Context: Current exoplanet formation studies tend to overlook the birth
environment of stars in clustered environments. The effect of this environment
on the planet-formation process, however, is important, especially in the
earliest stage. Aims: We investigate the differences in planet populations
forming in star-cluster environments through pebble accretion and compare these
results with the planet formation around isolated stars. We try to provide
potential signatures on the young planetary systems to guide future
observation. Methods: We design and present a new planet population synthesis
code for clustered environments. The planet formation model is based on pebble
accretion and includes migration in the circumstellar disk. The disk's gas and
dust are evolved in 1D simulations considering the effects of photo-evaporation
of the nearby stars. Results: Planetary systems in a clustered environment are
different than those born in isolation; the environmental effects are important
for a wide range of observable parameters and the eventual architecture of the
planetary systems. Planetary systems born in a clustered environment lack cold
Jupiters compared to isolated planetary systems. This effect is more pronounced
for low-mass stars ($\lesssim$0.2 $M_\odot$). On the other hand, planetary
systems born in clusters show an excess of cold Neptune around these low-mass
stars. Conclusions: In future observations, finding an excess of cold Neptunes
and a lack of cold Jupiters could be used to constrain the birth environments
of these planetary systems. Exploring the dependence of cold Jupiter's
intrinsic occurrence rate on stellar mass provides insights into the birth
environment of their proto-embryos.
