  In this paper, stellar hydrostatic equilibrium configuration of the compact
stars (neutron stars and strange stars) has been studied for $f(\mathcal{G},T)$
gravity model, with $\mathcal{G}$ and $T$ being the Gauss-Bonnet invariant and
the trace of energy momentum tensor, respectively. After having derived the
hydrostatic equilibrium equations for $f(\mathcal{G},T)$ gravity, the fluid
pressure for the neutron stars and the strange stars has been computed by
implying two equation of state models corresponding to two different existing
compact stars. For the $f(\mathcal{G},T)=\alpha{\mathcal{G}^n+\lambda{T}}$
gravity model, with $\alpha$, $n$, and $\lambda$ being some specific constants,
substantial change in the behavior of the physical attributes of the compact
stars like the energy density, pressure, stellar mass, and total radius has
been noted with the corresponding change in $\lambda$ values. Meanwhile, it has
been shown that for some fixed central energy density and with increasing
values of $\lambda$, the stellar mass both for the neutron stars and the
strange stars increases, while the total stellar radius $R$ exhibits the
opposite behavior for both of the compact stars. It is concluded that for this
$f(\mathcal{G},T)$ stellar model, the maximum stellar mass can be boosted above
the observational limits.
