  In this study, we explore several new characteristics of a static anisotropic
hybrid star with strange quark matter (SQM) and ordinary baryonic matter (OBM)
distribution. Here, we use the MIT bag model equation of state to connect the
density and pressure of SQM inside stars, whereas the linear equation of state
$p_r =\alpha \rho-\beta$ connects the radial pressure and matter density caused
by baryonic matter. The stellar model was developed under a background of
$f(Q)$ gravity using the quadratic form of $f(Q)$. We utilized the
Tolman-Kuchowicz ansatz to find the solutions to the field equations under
modified gravity. We have matched the interior solution to the external
Schwarzschild spacetime in order to acquire the numerical values of the model
parameters. We have selected the star Her X-1 to develop various profiles of
the model parameters. Several significant physical characteristics have been
examined analytically and graphically, including matter densities, tangential
and radial pressures, energy conditions, anisotropy factor, redshirt,
compactness, etc. The main finding is that there is no core singularity present
in the formations of the star under investigation. The nature of mass and the
bag constant $B_g$ have been studied in details through equi-mass and
equi-$B_g$ contour. The maximum allowable mass and the corresponding radius
have been obtained via $M-R$ plots.
