We have calculated the static and spherically symmetric solutions for compact
stars in the $f(\mathcal{R},T)$ gravity metric formalism. To describe the
matter of compact stars, we have used the MIT Bag model equation of state (EoS)
and the color-flavor-locked (CFL) EoS. Solving the hydrostatic equilibrium
equations i.e., the modified TOV equations in $f(\mathcal{R},T)$ gravity, we
have obtained different stellar models. The mass-radius profiles for such stars
are eventually discussed. The stability of these configurations are then
analysed using different parameters. From the obtained solutions of TOV
equations for mass and radius, we have checked the compactness of such objects.
It is found that similar to the unrealistic EoS, like the stiffer form of the
MIT Bag model, under some considerations the realistic interacting quark matter
CFL EoS can give stellar structures which are compact enough to possess a
photon sphere outside the stellar boundary and hence can echo GWs. The obtained
echo frequencies are found to lie in the range of 39-55 kHz. Also we have shown
that for different parametrizations of the gravity theory, the structure of
stars and also the echo frequencies differ significantly. Moreover, we have
constrained the pairing constant value $\beta$ from the perspective of emission
of echo frequencies. For the stiffer MIT Bag model $\beta\geq-2.474$ and for
the CFL phase with massless quark condition $\beta\geq-0.873$, whereas for the
massive case $\beta\geq-0.813$.
