We report a magnetic state in GaV₄Se₈ which emerges exclusively in samples with mesoscale polar domains and not in polar mono-domain crystals. It is manifested by a sharp anomaly in the magnetic susceptibility and the magnetic torque, distinct from other anomalies observed also in polar mono-domain samples upon transitions between the cycloidal, the Néel-type skyrmion lattice and the ferromagnetic states. We ascribe this additional transition to the transformation of distinct magnetic textures, confined to polar domain walls (DW), to the ferromagnetic (FM) state. The emergence of these DW-confined magnetic states is likely driven by the mismatch of different spin spirals, hosted by the adjacent domains. A clear anomaly in the magneto-current indicates that the DW-confined magnetic states also have strong contributions to the magnetoelectric response. We expect polar DWs to commonly host such confined magnetic edge states and, thus, offer a fertile ground to explore novel forms of magnetism.