Magnetism is widely considered to be a key ingredient of unconventional superconductivity.In contrast to cuprate high-temperature superconductors, antiferromagnetism in Fe-based superconductors (FeSCs) is characterized by a pair of magnetic propagation vectors 1, 2 . Consequently, three different types of magnetic order are possible. Of theses, only stripe-type spin-density wave (SSDW) and spin-charge-density wave (SCDW) orders have been observed 2-4 . 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-and Co-doped CaKFe 4 As 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 4 As 4 structure.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.