We assume that the recently reported excess over Standard Model expectations in the diphoton production is originated from a new scalar boson phi which interacts with photons through the coupling proportional to phi F^2. We obtain the cross section for semi-elastic production process pp-> p gamma p-> p phi q X by considering phi-photon-photon and phi-photon-Z couplings and discuss the constraints on the coupling parameters. We investigate the potential of the semi-elastic production process to probe phi-photon-photon and phi-photon-Z.