Magnetism is widely considered to be a key ingredient of unconventional superconductivity. In contrast to cuprate high-temperature superconductors, antiferromagnetism in most Fe-based superconductors (FeSCs) is characterized by a pair of magnetic propagation vectors, (π,0) and (0,π). Consequently, three different types of magnetic order are possible. Of these, only stripe-type spin-density wave (SSDW) and spin-charge-density wave (SCDW) orders have been observed. A realization of the proposed spin-vortex crystal (SVC) order is noticeably absent. We report a magnetic phase consistent with the hedgehog variation of SVC order in Ni-doped and Co-doped CaKFe 4As 4 based on thermodynamic, transport, structural and local magnetic probes combined with symmetry analysis. The exotic SVC phase is stabilized by the reduced symmetry of the CaKFe 4As 4 structure. Thus, our results suggest that the possible magnetic ground states in FeSCs have very similar energies, providing an enlarged configuration space for magnetic fluctuations to promote high-temperature superconductivity.