  Considering ten well-known relativistic mean field models, we invoke feeble
interaction between hadronic matter and fermionic dark matter (DM) $\chi$ via
new physics scalar ($\phi$) and vector ($\xi$) mediators in neutron star core,
thereby forming DM admixed neutron stars (DMANSs). The chosen masses of the DM
fermion ($m_{\chi}$) and the mediators ($m_{\phi}$ and $m_{\xi}$) are
consistent with the self-interaction constraint from Bullet cluster while their
respective couplings ($y_{\phi}$ and $y_{\xi}$) are also constrained by the
present day relic abundance. Assuming that both $\phi$ and $\xi$ contribute
equally to the relic abundance, we compute the equation of state of the DMANSs
and consequently their structural properties. We found that for a particular
(constant) DM density, the presence of lighter DM results in more massive
DMANSs with larger radius. In the light of the various recent constraints like
those from the massive pulsar PSR J0740+6620, the gravitational wave (GW170817)
data and the results of NICER experiments for PSR J0030+0451 and PSR
J0740+6620, we provide a bound on $m_{\chi}$ within the framework of the
present work as $m_{\chi}\approx$ (0.1 $-$ 30) GeV for a wide range of fixed DM
Fermi momenta $k_F^{\chi}$=(0.01 $-$ 0.07) GeV. In the case of the hadronic
models that yield larger radii corresponding to the low mass neutron stars in
the no-DM scenario, interaction with comparatively heavier DM fermion is
necessary in order to ensure that the DMANSs obtained with such models satisfy
the radius constraints from both GW170817 and NICER data for PSR J0030+0451.
