  $f(Q,T)$ theory of gravity is very recently proposed to incorporate within
the action Lagrangian, the trace $T$ of the energy-momentum tensor along with
the non-metricity scalar $Q$. The cosmological application of this theory in a
spatially flat isotropic and homogeneous Universe is well-studied. However, our
Universe is not isotropic since the Planck era and therefore to study a
complete evolution of the Universe we must investigate the $f(Q,T)$ theory in a
model with a small anisotropy. This motivated us to presume a locally
rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion
equations. We analyse the model candidate $f(Q,T)=\alpha Q^{n+1}+\beta T$, and
to constrain the parameter $n$, we employ the statistical Markov chain Monte
Carlo (MCMC) method with the Bayesian approach using two independent
observational datasets, namely, the Hubble datasets, and Type Ia supernovae
(SNe Ia) datasets.
