\begin{document}$R_{K}$\end{document} in rare semi-leptonic \begin{document}$B$\end{document}-meson decays and the present-day Hubble parameter \begin{document}$H_0$\end{document} in the Universe, implying tantalizing hints of new physics beyond the standard model. In this paper, we consider a simple flavor-specific two-Higgs-doublet model, where long-standing \begin{document}$R_{K^{(*)}}$\end{document} anomalies can be addressed by a one-flavor right-handed neutrino. An intriguing prediction resulting from the parameter space for the \begin{document}$R_{K^{(*)}}$\end{document} resolution under flavor- and collider-physics constraints points toward a shift in the effective neutrino number, \begin{document}$\Delta N_{\rm eff}=N_{\rm eff}-N_{\rm eff}^{\rm SM}$\end{document}, as a favored way to ease the \begin{document}$H_0$\end{document} tension. Depending on whether the neutrino is of the Dirac or Majorana type, we show that the resulting shift is \begin{document}$\Delta N_{\rm eff}\simeq 1.0$\end{document} for the former case and \begin{document}$\Delta N_{\rm eff}\simeq 0.5$\end{document} for the latter case. While the Dirac case is disfavored by the CMB polarization measurements, the Majorana solution is consistent with recent studies using a combined dataset from various sources. Consequently, such a simple flavor-specific two-Higgs-doublet model provides a link between \begin{document}$R_{K^{(*)}}$\end{document} anomalies and \begin{document}$H_0$\end{document} tension, which in turn can be readily verified or disproved by upcoming measurements."> Linking <inline-formula><tex-math id="Z-20221230105040">\begin{document}${ {\boldsymbol R}_{{\boldsymbol K}^{\boldsymbol{(*)}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/251beb4f-7b62-49e6-9ba6-061d52cc13c4/CPC-2022-0489_Z-20221230105040.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/251beb4f-7b62-49e6-9ba6-061d52cc13c4/CPC-2022-0489_Z-20221230105040.png"/></alternatives></inline-formula>anomalies to Hubble tension via a single right-handed neutrino -
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