  This cosmological model is a study of modified $f(Q,T)$ theory of gravity
which was recently proposed by Xu {\it et al.} (Eur. Phys. J. C {\bf 79}, 708
(2019)). In this theory of gravity, the action contains an arbitrary function
$f(Q,T)$ where $Q$ is non-metricity and $T$ is the trace of energy-momentum
tensor for matter fluid. In our research, we have taken the function $f(Q,T)$
quadratic in $Q$ and linear in $T$ as $f(Q,T)=\alpha Q+\beta Q^{2}+\gamma T$
where $\alpha$, $\beta$ and $\gamma$ are model parameters, motivated by
$f(R,T)$ gravity. We have obtained the various cosmological parameters in
Friedmann-Lemaitre-Robertson-walker (FLRW) Universe viz. Hubble parameter $H$,
deceleration parameter $q$ etc. in terms of scale-factor as well as in terms of
redshift $z$ by constraining energy-conservation law. For observational
constraints on the model, we have obtained the best-fit values of model
parameters using the available data sets like Hubble data sets $H(z)$, Joint
Light Curve Analysis (JLA) data sets and union $2.1$ compilation of SNe Ia data
sets by applying $R^{2}$-test formula. We have calculated the present values of
various observational parameters viz. $H_{0}$, $q_{0}$, $t_{0}$ and statefinder
parameters $(s,r)$, these values are very close to the standard cosmological
models. Also, we have observed that the deceleration parameter $q(z)$ shows
signature-flipping (transition) point within the range $0.423\leq
z_{t}\leq0.668$ through which it changes its phase from decelerated to
accelerated expanding universe with equation of state (EoS)
$-1.071\leq\omega-0.96$ for $0\leq z\leq3$.
