  We investigate the impact of $f(R,L_m,T)$ gravity on the internal structure
of compact stars, expecting this theory to manifest prominently in the
high-density cores of such stars. In this study, we begin by considering the
algebraic function $f(R,L_m,T) = R + \alpha T L_m$, where $\alpha$ represents
the matter-geometry coupling constant. We specifically choose the matter
Lagrangian density $L_m= -\rho$ to explore compact stars with anisotropic
pressure. To this end, we employ the MIT bag model as an equation of state. We
then numerically solve the hydrostatic equilibrium equations to obtain
mass-radius relations for quark stars, examining static stability criteria, the
adiabatic index, and the speed of sound. Finally, we use recent astrophysical
data to constrain the coupling parameter $\alpha$, which may lead to either
larger or smaller masses for quark stars compared to their counterparts in
general relativity.
