[en] In the present communication, we report a model Hamiltonian to study the interplay between the two long range orders of anti-ferromagnetism (AFM) and superconductivity (SC) in cuprate superconductors in presence of the intersite pairing effect. The BCS type but non-phonon pairing mechanism is considered among the electrons of two equivalent Cu sites. The pairing among the electrons of two nearest neighbour non-equivalent Cu sites is included in the Hamiltonian and its effect on the interplay of SC and AFM is investigated. The Hamiltonian is solved by the Green's function method and the corresponding gap equations are calculated and solved self-consistently. The influence of model parameters like AFM coupling (λ), SC coupling (λ₁) and the coupling (λ₂) for intersite superconducting interactions on the gaps (SC and AFM) are studied numerically and the results are reported. (author)