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This work aims to characterize printing structures with various infill densities composed of a thermoplastic material containing magnetic particles composed of mainly Iron(III) oxides with regard to their possible processing with the additive technology of Fused Filament Fabrication. A polyethylene terephthalate glycol (PET-G) structural thermoplastic with the addition of Iron(III)) oxides has been selected, and correct processing temperatures have been determined using thermal analysis. The paramagnetic properties of printed products consisting of different filling densities have been tested. Relative permeability has been identified to be strongly dependent on the printed internal structures of tested products. The samples composed of the densest structure have shown relative permeability higher by 18% with respect to the sample printed with the least dense structure. Finite Element Modelling (FEM) simulations have been applied to determine magnetic field distributions and, moreover, to calculate the holding forces of all printed samples. The performed simulations confirmed that produced composites might be utilized as magnetic switches and sensors or as more advanced components for homogenizing electric motors’ magnetic fields. Moreover, magnetic properties might be tuned according to the specific needs printing structure with the suitable density.