Quintom-like transit universe models in Metric-affine $f(R,T,Q,T_m)$ gravity

The current transit universe model is a precise solution to the equations of a new type of gravity theory called metric-affine $f(R,T,Q,T_m)$ gravity proposed in [Herko et al. $\mathit{\text{Phys.}}\mathit{\text{Dark}}\mathit{\text{Univ.}}$ $\mathbf{\text{34}}$ (2021) 100886]. This theory is the maximal extension of the most successful theory, General Relativity," by including the scalars, Ricci curvature $R$, torsion $T$, nonmetricity $Q$, and trace $T_{m}$ of the matter-energy-momentum tensor using a generalized connection called the metric-affine" connection. We obtain the modified field equations for a linear form of the $f(R,T,Q,T_m)$ function and for a flat, homogeneous, and isotropic FLRW spacetime universe. We find a hyperbolic solution and determine the constrained values of the model parameters using the latest observational data. We examine how certain cosmological factors, like the deceleration parameter $q(z)$, effective equation of state parameter ${\omega }_{\mathrm{e}\mathrm{f}\mathrm{f}}$, and dark energy equation of state parameter ${\omega }_{\mathrm{d}\mathrm{e}}$, vary over time to explain the properties of the observable universe. We perform the $Om$ diagnostic test for the model, and it represents the phantom scenarios of the model. The behavior of the dark energy EoS parameter ${\omega }_{\mathrm{d}\mathrm{e}}$ reveals the quintom-A-type universe characteristics.