We have examined the atomic coordination effect on the local bond strain and the 3p core-level shift of K(110) skin and nanoclusters using a combination of the bond order-length-strength correlation notion, tight-binding approach, density functional theory calculations, and photoelectron spectroscopy measurements. It turns out that: (i) the 3p core-level shifts from 15.595 ± 0.003 eV for an isolated K atom by 2.758 eV to the bulk value of 18.353 eV; (ii) the effective atomic coordination number reduces from the bulk value of 12 to 3.93 for the first layer and to 5.81 for the second layer of K(110) skin associated with the local lattice strain of 12.76%, a binding energy density 72.67%, and atomic cohesive energy -62.46% for the skin; and, (iii) K cluster size reduction lowers the effective atomic coordination number and enhances further the skin electronic attribution. Results have revealed that the 3p core-level shifts of K(110) and nanoclusters originate from perturbation of the Hamiltonian by under-coordination induced charge densification and quantum entrapment.