\begin{document}$ {D}_{\left(s\right)}^{+}\to {\eta }^{\left({'}\right)}\overline{l}{\nu }_{l} $\end{document} decays, which deviate from their SM predictions, we hve investigated these decays in \begin{document}${W}'$\end{document} model and scalar leptoquark model to determine potential signatures of new physics (NP) in semileptonic charm decays induced by \begin{document}$ c\to (s,d)\overline{l}{\nu }_{l} $\end{document} transitions. Using recent experimental results of branching fractions for semileptonic \begin{document}$ D $\end{document} meson decays, new coupling parameters are predicted for the aforementioned NP models. Branching fraction, forward-backward asymmetry, and lepton polarization asymmetry are examined by considering the predicted NP coupling parameters. The results of branching fractions in scalar leptoquark model are found very close to the experimental results and exist around the range of \begin{document}$ 1\sigma $\end{document} deviation. We presented a comparative study of the NP models to check their sensitivity on these decays. We anticipate that further research on these decays will significantly support our findings."> Model dependent analysis of <inline-formula><tex-math id="Z-20240723204927">\begin{document}$ {\boldsymbol D_{(\boldsymbol s)}^{\bf +} \to \boldsymbol\eta^{(')}\boldsymbol l^{\bf +}{\boldsymbol v}_{\boldsymbol l}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/41925acf-ad1c-4639-9ccd-520a8a72b29a/CPC-2024-0208_Z-20240723204927.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/41925acf-ad1c-4639-9ccd-520a8a72b29a/CPC-2024-0208_Z-20240723204927.png"/></alternatives></inline-formula> decays in beyond standard model -
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