This paper presents the results of a research project aimed at evaluating the unconventional natural gas potential of the autochthonous Miocene sediments in the Polish part of the Carpathian Foredeep. The primary objective of the study was to re-evaluate the biogenic gas generation system within Miocene sediments, paying special attention to unconventional gas resources accumulated in tight mudstone formations. The four-dimensional (4D) petroleum system modeling method (PetroMod software) was used to reconstruct the basin geometry and three-dimensional (3D) evolution through a geological timescale, in particular the progress of gas generation, migration, and accumulation processes, as well as their consequences for gas exploration and development. Special attention was paid to the dynamics of gas generation processes and the advancement of sediment compaction and their time dependence, as well as to the progress and outcomes of gas migration and accumulation processes. The results indicate significant potential for unconventional gas accumulations in mudstone reservoirs. However, part of the biogenic gas resources occurs in a dispersed form. Analysis of the dynamics of biogenic gas generation and accumulation conducted on a basin scale and within particular sedimentary complexes and depth intervals allowed an indication of the premises regarding the most favorable zones for mudstone–claystone reservoir exploration.