The Kittel-Shore (KS) Hamiltonian describes N spins with long-range interactions that are identically coupled. In this paper (arXiv:2502.20884) , the underlying 𝔰𝔲(2) coalgebra symmetry of the KS model is demonstrated for arbitrary spins, and the quantum deformation of the KS Hamiltonian (q-KS model) is obtained using the corresponding 𝔰𝔲_q(2) quantum group. By construction, the existence of such a symmetry guarantees that all integrability properties of the KS model are preserved under q-deformation. In particular, the q-KS model for spin-1/2 particles is analysed in both ferromagnetic and antiferromagnetic couplings, and the cases with N=2,3, and 4 spins are studied in detail. The higher-spin q-KS models are sketched.