  We propose a novel cosmological framework within the $f(R,T)$ type modified
gravity theory, incorporating a non-minimally coupled with the higher order of
the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor
($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m +
2 \lambda T^n$, where $\lambda$, $m$, and $n$ are arbitrary constants. Taking a
constant jerk parameter ($j$), we derive expressions for the deceleration
parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift
$z$. We constrained our model with the recent Observational Hubble Dataset
(OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of
Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by
late-time acceleration, with the transition occurring in the redshift range
$1.10 \leq z_{tr} \leq 1.15$. Our findings suggest that this higher-order model
of $f(R,T)$ gravity theory can efficiently provide a dark energy model for
addressing the current scenario of cosmic acceleration.
