and mixing constraints on the model parameters, taking into account three generations of light neutrinos. We explicitly show the hierarchical structure of Dirac mass matrix. We also analyze the potential and evaluate the Higgs spectrum in detail. Furthermore, with the set of model parameters that satisfy neutrino oscillation measurements, we carry out an in-depth analysis of the pair-production and decay of these charged scalars in the upcoming International Linear Collider (ILC) and Compact Linear Collider (CLIC) experiments. The final state of two opposite sign leptons and missing energy can be measured quite significantly over the SM background resulting in a possibility to observe such a process even with a very low luminosity $\mathcal{L} \sim 1-3 \, \rm{fb}^{-1}$ at these experiments. Therefore, even an early run of ILC/CLIC can detect the presence of such a gauge singlet charged Higgs state. The rest of this paper is organized as follows. We discuss the model and the particle spectrum in Section. \[model\]. Following that, the pair-production of the charged Higgs and its detailed collider phenomenology is discussed in Section. \[col\]. We present our conclusions in Section. \[conc\].

Model and Spectrum {#model}
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LRS models are simple gauge extensions of the SM with the 