  The influence of the dark matter mass~($M_{\chi}$) and the Fermi
momentum~($k_{F}^{\dm}$) on the $f_0$-mode oscillation frequency, damping time
parameter, and tidal deformability of hadronic stars are studied by employing a
numerical integration of hydrostatic equilibrium, nonradial oscillation, and
tidal deformability equations. The matter inside the hadronic stars follows the
NL3* equation of state. We obtain that the influence of $M_{\chi}$ and
$k_F^{\dm}$ is observed in the $f_0$-mode, damping tome parameter, and tidal
deformability. Finally, the correlation between the tidal deformability of the
GW$170817$ event with $M_{\chi}$ and $k_F^{\dm}$ are also investigated.
