  We investigate anisotropic quark stars within the context of energy-momentum
squared gravity (EMSG), assuming the internal composition consists of
homogeneous, charge-neutral 3-flavor interacting quark matter with ${\cal
O}(m_s^4)$ corrections. We performed numerical calculations of the equation of
state (EoS) and the modified Tolman-Oppenheimer-Volkoff (TOV) structure
equation. Additionally, we discussed the impact of the GB coupling parameter
$\alpha $ on the mass-radius relationship. Furthermore, we compared our results
with astronomical observational data. Our research offers a new perspective,
proposing that in EMSG, accounting for anisotropy could lead to denser stars
than in isotropic scenarios.

General Relativity and Quantum Cosmology