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Today, most of the innovative composite materials are made of cross-linked polymers, which include epoxy resins. They are widely used to construct different parts of aircraft, transport vehicles and electronic devices. The combination of epoxy resins, which are liquids in an uncured state, and magnetic nanoparticles (MNPs) opens up new ways for creating new advanced nanomaterials. The magnetic field makes it possible to order nanoparticles. The curing reaction can be used to "record" the resulting structure. To implement such materials, in addition to direct experimental studies, it is essential to develop theoretical models capable of predicting the structure and physical properties of the epoxy nanocomposites with embedded MNPs. This report discusses a coarse-grained model of a polymer nanocomposite based on a highly cross-linked polymer matrix filled with MNPs. To simulate MNPs, we propose a model in which they are represented as a set of bonded magnetic dipoles. It is assumed that nanoparticles are not connected to the polymer matrix. Thus, during mechanical deformations, the nanofiller can transfer the load only through non-bonded interactions with a polymer. All simulations were performed using a reactive dissipative particle dynamics (DPD) method, in which the interaction of MNPs with an external magnetic field is added. We use the developed model to investigate the magnetic field's effect on the structure and mechanical properties of a magnetoresponsive nanocomposite based on a highly cross-linked polymer with embedded MNPs. The polymer network formation from polymerizing monomers was simulated both in the magnetic field and without it. The DGEBA epoxy resin, tricarboxylic acid as the hardener, and the magnetite nanoparticles were selected as prototypes of real chemical structures. Under the field's influence, the MNPs form filamentous aggregates drawn out along the field strength lines that induce the polymer matrix's anisotropic structure and affect the network topology. The stress-strain curves demonstrate that the ordering of MNPs also causes anisotropy of mechanical properties and leads to an increase in Young's modulus for uniaxial tension along the long aggregate axis. When monomers polymerize in the presence of MNPs at zero applied field, the filler particles remain disordered, and Young's modulus of such a composite can exhibit a slight linear decrease with increasing filler content. This behavior is well attributed to the reduction in the number of load-bearing chains in the simulation box. Additionally, the role of the polymer/MNP interface is discussed.