Ion channels, such as potassium channels are known to discriminate ions to achieve remarkable selective transportation of K+ over Na+ through the membrane. The recently reported NaK ion channel, on the contrary, seems to be an exception, as it is observed to permeate most of the group IA alkali metal cations and hence is suggested to be nonselective in nature. However, does that correspond to a complete annihilation of selectivity inside the selectivity filter (SF) of the channel? What is the origin of such nonselectivity/selectivity, if any? The present computational study is an extensive multiscale modeling approach to find the probable answers to these intriguing questions. Here, we have used density functional theory (DFT) based calculations using a realistic truncated model of SF from the crystal structures of the NaK ion channel to evaluate the binding of various alkali metal ions (Na+, K+ and Cs+), free from "contamination" due to the absence any other "rivalry" cations, in its different binding sites. Among all of the possible binding sites, a vestibule is noticed to be nonselective and seen to act as a probable binding site only in the presence of multiple ions. Binding sites S3 and S4 are found to be selective for K+ and Na+, may lead to an erroneous selectivity trend as it neglects the synergetics of consecutive binding sites on the final outcome. Energy decomposition analysis revealed ion-dipole electrostatics as the major contributing interaction in metal-bound binding sites. Our investigations find that although NaK is permeable to monovalent alkali metal ions, strongly "site specific" selectivity does exist at the three well-defined noncontiguous binding sites of the SF. Different important physicomechanical parameters (such as ligating environment, synergistic influence of binding sites, and topological constraints) are found to be the determining factor to induce the "site specific" selectivity of ions during translocation. Wherever possible, our computed results are compared with the available experimental findings. We finally conduct a detailed umbrella sampling-corrected metadynamics simulation in order to obtain an ion permeation free energy landscape within the SF that corroborates well with the "site specific" selectivity trend.