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We investigate the structure of admixed neutron stars with a regular hadroniccomponent and a fraction of fermionic self-interacting dark matter. Using twolimiting equations of state for the dense baryonic interior, constructed frompiecewise generalised polytropes, and an asymmetric self-interacting fermionicdark component, we analyse different scenarios of admixed neutron starsdepending on the mass of dark fermions $m_\chi$, interaction mediators$m_\phi$, and self-interacting strengths $g$. We find that the contribution ofdark matter to the masses and radii of neutron stars leads to tension with massestimates of the pulsar J0453+1559, the least massive neutron star, and withthe constraints coming from the GW170817 event. We discuss the possibilities ofconstraining dark matter model parameters $g$ and $y \equiv m_\chi/m_\phi$,using current existing knowledge on neutron star estimations of mass, radius,and tidal deformability, along with the accepted cosmological dark matterfreeze-out values and self-interaction cross-section to mass ratio,$\sigma_\mathrm{SI}/m_\chi$, fitted to explain Bullet, Abell, and dwarf galaxycluster dynamics. By assuming the most restrictive upper limit,$\sigma_\mathrm{SI}/m_\chi < 0.1$ cm$^2$/g, along with dark matter freeze-outrange values, the allowed $g$-$y$ region is $0.01 \lesssim g \lesssim 0.1$,with $0.5 \lesssim y \lesssim 200$. For the first time, the combination ofupdated complementary restrictions is used to set constraints onself-interacting dark matter.

Constraining self-interacting fermionic dark matter in admixed neutron stars using multimessenger astronomy