The paper presents the results of the computational modeling and quantum-chemical investigations of metal-polymer composites based on pyrolyzed polyacrylonitrile (PAN) consisting of the ternary Fe–Ni–Co compound. The proposed model of pyrolyzed PAN monolayer contains three atoms of iron, nickel, and cobalt instead of eight atoms of the basal polymer substance. Determined are the geometry and electronic and energetic properties of the nanocomposite. It is found that the introduction of the metal atoms leads to a decrease in the energy gap of the metal-polymer composite due to the layer formation of the interstitial metal atoms (nickel, cobalt) in the valence band or at the conduction band edge (iron), which, in turn, modifies the conductive properties of the obtained nanocomposite. The analysis of the charge redistribution in the system shows that in applying the electric field, the appeared charge carriers contribute to the ordered motion of free charged particles in the metal-polymer composite, thereby changing its magnetic properties.