  The formulation of quarkyonic matter consists of treating both quarks and
nucleons as quasi-particles, where a cross-over transition occurs between the
two phases. This work is based upon some of the early ideas of quark matter. It
can satisfy the different observational constraints on the neutron star (NS),
such as its maximum mass and the canonical radius. In addition, we put an extra
component inside the NS known as Dark Matter (DM) because it is trapped due to
its immense gravitational potential. In this work, we explore the impact of
fermionic DM on the structure of the NS. The equation of state (EOS) is derived
for the NS with the quarkyonic matter by assuming that nucleons and quarks are
in equilibrium, followed by the relativistic mean-field (RMF) formalism. The
recently modeled two parameterizations, such as G3 and IOPB-I, are taken to
calculate the various macroscopic properties of the NS. The three unknown
parameters such as the transition density ($n_t$), the QCD confinement scale
($\Lambda_{\rm sc}$), and the DM Fermi momentum ($k_f^{\rm DM}$) are varied to
obtain the NS properties. The quarkyonic matter stiffens the EOS while DM
softens it. The mutual combination provides us with good theoretical
predictions for the magnitude of macroscopic properties consistent with the
different observational results. Also, one can estimate the parameters of the
DM admixed quarkyonic star with different statistical analyses, which can be
further used to explore the other properties of the quarkyonic star.
