  We conduct a Bayesian analysis of recent observational datasets, specifically
the Cosmic Chronometers (CC) dataset and Pantheon samples, to investigate the
evolution of the EoS parameter in dark energy models. Our study focused on the
effective EoS parameter, which is described by the parametric form
$\omega_{eff}=-\frac{1}{1+m(1+z)^n}$, where $m$ and $n$ are model parameters.
This parametric form is applicable within the framework of $f(R,L_m)$ gravity,
where $R$ represents the Ricci scalar and $L_m$ is the matter Lagrangian. Here,
we examine a non-linear $f(R,L_m)$ model characterized by the functional form
$f(R,L_m)=\frac{R}{2}+L_m^\alpha$, where $\alpha$ is the free parameter of the
model. We examine the evolution of several cosmological parameters, including
the effective EoS parameter $\omega_{eff}$, the deceleration parameter $q$, the
density parameter $\rho$, the pressure $p$, and the statefinder parameters. Our
analysis revealed that the constrained current value of the effective EoS
parameter, $\omega_{eff}^{0}=-0.68\pm0.06$ for both the CC and Pantheon
datasets, points towards a quintessence phase. Moreover, at redshift $z=0$, the
deceleration parameter, $q_0 = -0.61^{+0.01}_{-0.01}$, indicates that the
present Universe is undergoing accelerated expansion.
