  Recent experimental measurements on the anomalies observed in B meson decays
have pointed towards the possibility of new physics. The LHCb collaboration has
reported a significant deviation, exceeding $3.2\sigma$, from the predictions
of the standard model. This discrepancy is observed in the combined measurement
on the ratio of branching ratio $R(D)-R(D^\star)$ for the decays corresponding
to $B\to D\ell\nu$ and $B\to D^\star\ell\nu$ processes. Furthermore, the other
observables, such as $R_{J/\psi}$, $P_{\tau}^{D^\star}$, $F_L^{D^\star}$, and
$R_{\Lambda_c}$ in the $b\to c\ell\nu$ transition, have also exhibited
noticeable deviations from the standard model predictions. Motivated by these
anomalies in the $b\to c\tau\nu$ transitions, we perform a log-likelihood fit
incorporating new physics scalar couplings and explored the implications of a
charged Higgs boson within a generic two Higgs doublet model. Our comprehensive
analysis, focused on the $\tau\nu$ and $b\tau\nu$ final states, was performed
using the High Luminosity run of the Large Hadron Collider (HL-LHC). We
demonstrate the sensitivity of the collider search for a low-mass charged Higgs
boson while considering the current experimental constraints on various $b\to
c\tau\nu$ flavor observables.
