In this work we study the production of a dark matter (DM) particle in association with a Higgs boson via a central exclusive photon-fusion initiated process. We explore this type of production through the Inert Doublet Model plus a Scalar (IDMS), where an extension of the Standard Model by an additional $U(1)\chi$ gauge symmetry and a $SU(2)$ scalar doublet gives rise to a DM candidate. This particular process involves the collision of two protons exchanging two colorless particles (in our case, photons), from which a central process occurs. Such interaction can be detected in the LHC using forward proton detectors, where the resulting missing mass spectrum can be observed after proton reconstruction, thus allowing a search for physics Beyond the Standard Model (BSM). We present results with different values of $\Delta = m_S - m\chi - m_H$, which is the phase space available for the final state in the central exclusive process.