  The equation of state (EOS) for neutron stars is modeled using the
Relativistic Mean Field (RMF) approach with a mesonic nonlinear (NL)
interaction, a modified sigma cut potential (NL-$\sigma$ cut), and the
influences of dark matter in the NL (NL DM). Using a Bayesian analysis
framework, we evaluate the plausibility and impact of each scenario.
Experimental constraints on the general properties of finite nuclei and heavy
ion collisions, along with astrophysical observational data on neutron star
radii and tidal deformation, have been taken into account. It was shown that
all models, including the PREX-II data, were less favored, indicating that this
experimental data seemed to be in tension with the other constraints included
in the inference procedure, and were incompatible with chiral effective field
theoretical calculations of pure neutron matter. Considering the models with no
PREX-II constraints, we find the model NL-$\sigma$ cut with the largest Bayes
evidence, indicating that the constraints considered favor the stiffening of
the EOS at large densities. Conversely, the neutron star with a dark matter
component is the least favorable case in light of recent observational
constraints, among different scenarios considered here. The $f$ and $p$ modes
were calculated within the Cowling approximation, and it can be seen that $f$
modes are sensitive to the EOS. An analysis of the slopes of the mass-radius
curves and $f$-mode mass curves has indicated that these quantities may help
distinguish the different scenarios.We also analyzed the impact of new PSR
J0437-4715 measurements on neutron star mass-radius estimates, noting a $\sim$
0.2 km reduction in the 90\% CI upper boundary across all models and a
significant Bayes evidence decrease, indicating potential conflicts with
previous data or the necessity for more adaptable models.
