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In this research paper, we consider the process of neutral Higgs production from e+e– annihilation in Inert Higgs Doublet Model (IHDM) in the absence and presence of an external field. The latter is assumed to be a plane and monochromatic wave with linear polarization. In the theoretical framework, we present the analytic calculation of the lowest order differential cross section by using the scattering matrix approach and Dirac–Volkov formalism for charged incident particles. The total cross section is computed by performing a numerical integration of the differential cross section over the solid angle. The results obtained are analyzed and discussed for different centre of mass energies and laser parameters. We found that inserting a laser wave with linear polarization is a suitable mechanism to enhance the total cross section of the process. Indeed, the probability of the process to occur increases with the presence of a linearly polarized laser field, especially with low frequency and high strength. [ABSTRACT FROM AUTHOR]