Claudins are tissue-specific transmembrane proteins able to form junctions between two cells and regulate the flow of physiological solutes parallel to the cell walls, that is, the paracellular transport. Claudin-15 is highly expressed in the intestine where it forms efficient Na+ channels and Cl- barriers. However, the molecular details of these biological complexes are still unclear. Here, the permeation process of Na+, K+, and Cl- ions inside a refined structural model of a claudin-15 paracellular channel is investigated using all-atom molecular dynamics simulations in a double-bilayer and explicit solvent. One-dimensional potential of mean force (PMF) profiles, calculated using umbrella sampling (US) simulations, show that the channel allows the passage of the two physiological cations while excluding chloride. These features are generated by the action of several acidic residues, in particular the ring of D55 residues which is located at the narrowest region of the pore, in correspondence with the energy minimum for cations and the peak for chloride. We also used the Voronoi-tessellated milestoning method to obtain additional PMF profiles and the permeation timescale of the three ions. The milestoning PMFs agree well with those obtained by US, and the rate calculation reveals that the passage of chloride is almost 30 times slower than that of sodium. Our results are consistent with the known ability of claudin-15 to regulate tight junction selectivity and with the experimentally determined role of the acidic residues. This further validates our structural model and provides insights into the atomistic details of ion transport in paracellular channels that could be shared by other claudin-based architectures.