Adsorption and mobility of radioactive Cs+ isotopes in soil are among the most important factors affecting the long-term environmental footprint of nuclear accidents such as Chernobyl (1986) and Fukushima Daiichi (2011). In particular, Cs+ ions can be retained through their exchange with K+ naturally present in muscovite mica, one of the common soil mineral components. The ClayFF force field allowed us to realistically represent local inhomogeneities of the structure, composition, and charge on the muscovite (001) surface and to identify three structurally different types of adsorption sites. We performed molecular dynamics simulations of Cs+ and K+ adsorption at the hydrated muscovite surface and used quasi-one-dimensional site-specific potential of mean force calculations to quantify the energetics of ion exchange in this system for each individual site and for the entire muscovite surface on average. Irrespective of the type of adsorption site, both K+ and Cs+ cations are preferably adsorbed on the basal (001) muscovite surface at the centers of ditrigonal cavities as inner sphere surface complexes. The free energy difference between the most favorable and the least favorable surface sites for Cs+/K+ ion exchange amounts to 11.7 kJ/mol, with the most favorable sites occupying half of the surface and the least favorable type - 1/6 of the surface and the rest exhibiting an intermediate adsorption and ion exchange capacity. The simulation results are compared with available thermodynamic estimates based on recent X-ray reflectivity measurements.