Context. Current exoplanet formation studies tend to overlook the birth environment of stars in clustered environments. However, the effects of this environment on the planet formation process are 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 planet formation around isolated stars. We strive to provide potential signatures of the young planetary systems to guide future observations. Methods. We present a new planet population synthesis code designed for clustered environments. This planet formation model is based on pebble accretion and includes migration in the circumstellar disk. The disk’s gas and dust have been evolved via 1D simulations, while 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, as compared to isolated planetary systems. This effect is more pronounced for low-mass stars (≲0.2 M⊙). 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 offers insights into the birth environment of their proto-embryos.