  In this work we present a theoretical investigation into an
antiferromagnetically coupled spin system, specifically ${\rm Cu}_{3}-X$
($\mathrm{X=As,Sb}$), which exhibits an isosceles triangular configuration or
slightly distorted equilateral triangular configuration, as previously
identified in reference {[}Phys. Rev. Lett. \textbf{96}, 107202 (2006){]}. This
system can be effectively represented by the Heisenberg model on a triangular
structure, taking into account the exchange interaction, the
Dzyaloshinskii-Moriya interaction, g-factors and external magnetic field, as
delineated in the aforementioned reference. By using numerical approach we
explore both zero-temperature and finite-temperature behaviors of a ${\rm
Cu}_{3}$-like antiferromagnetically coupled spin system. At zero temperature,
the system displays a 1/3 quasi-plateau magnetization, when the magnetic field
is varied. Moreover, we place particular emphasis on magnetic properties
including magnetization, magnetic susceptibility, entropy, and specific heat at
finite temperatures. Furthermore, we investigate the magnetocaloric effect as a
function of an externally imposed magnetic field, oriented both parallel and
perpendicular to the plane of the triangular structure. Interestingly, these
configurations demonstrate remarkably similar behavior for both orientations of
the magnetic field. Our investigation also includes an analysis of the
adiabatic curve, the Gr\"uneisen parameter, and the variation in entropy when
applied or removed the magnetic field. The magnetocaloric effect is found to be
more prominent in low the temperature region, typically at $T\sim1$K, for both
parallel and perpendicular magnetic fields at $\sim4.5$T and $\sim5$T,
respectively.
