  The variety of theories that can account for the dark energy phenomenon
encourages current research to concentrate on a more in-depth examination of
the potential impacts of modified gravity on both local and cosmic scales. We
discuss some cosmological reconstruction in $f(Q,T)$ cosmology (where $Q$ is
the non-metricity scalar, and $T$ is the trace of the energy-momentum tensor)
corresponding to the evolution background in
Friedmann-La\^imatre-Robertson-Walker (FLRW) universe. This helps us to
determine how any FLRW cosmology can arise from a specific $f(Q,T)$ theory. We
use the reconstruction technique to derive explicit forms of $f(Q,T)$
Lagrangian for the different kinds of matter sources and Einstein's static
universe. We also formulate the models using several ansatz forms of the
$f(Q,T)$ function for $p=\omega \rho$. We demonstrate that several classes of
$f(Q,T)$ theories admit the power-law and de-Sitter solutions in some ranges of
$\omega$. Additionally, we reconstruct the cosmological model for the scalar
field with a specific form of $f(Q,T)$. These new models with cosmological
inspiration may impact gravitational phenomena at other cosmological scales.
