||We use a Monte Carlo simulation to investigate the magnetic structures in a bilayer magnetic system containing a locally inverted interlayer coupling region. The stabilization of multiple magnetic structures, including the magnetic skyrmion, is possible in the locally inverted interlayer coupling region. Various factors such as the region area, anisotropy, interlayer coupling strength, and exchange coupling strength affect the properties of the structures, including their size and chirality. We obtain conditions for the stabilization and transitions of these magnetic structures. The Dzyaloshinskii-Moriya interaction (DMI) and dipolar interaction play prominent roles as they significantly enhance the formation and stability of the structures. An asymmetric feature can arise from the broken inversion symmetry in the structure formation, yielding an interfacial DMI, which stabilizes the skyrmion. It is demonstrated that the dipole interaction also acts as an effective interfacial DMI in the system.