  In this paper, we have studied flat
Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW) model with modified
Chaplygin gas (MCG) having equation of state $p_{m}=A\rho -% \frac{B}{\rho
^{\gamma }}$, where $0\leq A\leq 1$, $0\leq \gamma \leq 1$ and $B$ is any
positive constant in }${\footnotesize f(R,T)}${\footnotesize \ gravity with
particle creation. We have considered a simple parametrization of the Hubble
parameter $H$ in order to solve the field equations and discussed the time
evolution of different cosmological parameters for some obtained models showing
unique behavior of scale factor. We have also discussed the statefinder
diagnostic pair $\{r,s\}$ that characterizes the evolution of obtained models
and explore their stability. The physical consequences of the models and their
kinematic behaviors have also been scrutinized here in some detail.
