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Type-X two Higgs doublet model is known to explain the muon $g-2$ anomalywith a relatively light charged Higgs boson at large $\tan\beta$. The lightcharged Higgs boson has been searched in the main $\tau \nu$ mode at thecolliders. Invoking a scenario of inverse seesaw as the origin of neutrinomasses and mixing, the charged Higgs boson can decay additionally toright-handed neutrinos which leads to interesting phenomenology. Consideringgeneric lepton flavour violating signatures at the final states, a $5\sigma$discovery can be achieved with the early data of LHC, at 14 TeV, for relativelylarge inverse seesaw Yukawa coupling $Y_N$. The very light pseudoscalar andcharged Higgs boson mass reconstruction are performed using the new modes andthe results look promising. The inverse seesaw Yukawa coupling is shown to beprobed down to $Y_N \sim 0.2$ at HL LHC with 3000 fb$^{-1}$.

Phenomenology of Higgs bosons in inverse seesaw model with Type-X two Higgs doublet at the LHC