We study the dark matter (DM) effects on the nuclear matter (NM) parameters characterizing the equation of states of super dense neutron-rich nucleonic matter. The observables of the NM, i.e. incompressibility, symmetry energy and its higher order derivatives in the presence DM for symmetric and asymmetric NM are analysed with the help of an extended relativistic mean field model. The calculations are also extended to β-stable matter to explore the properties of the neutron star (NS). We analyse the DM effects on symmetric NM, pure neutron matter, and NS using NL3, G3, and IOPB-I forces. The binding energy per particle and pressure is calculated with and without considering the DM interaction with the NM systems. The influences of DM are also analysed on the symmetry energy and its different coefficients. The incompressibility and the skewness parameters are affected considerably due to the presence of DM in the NM medium. We extend the calculations to the NS and find its mass, radius and the moment of inertia for static and rotating NS with and without DM contribution. The mass of the rotating NS is considerably changing due to rapid rotation with the frequency in the mass-shedding limit. The effects of DM are found to be important for some of the NM parameters, which are crucial for the properties of astrophysical objects.