<p>Topological defects give rise to non-trivial excitations—such as solitons, vortices and skyrmions—characterized by integer-valued topological charges. However, their classification becomes difficult when singularities are present in the order parameter field, complicating the computation of these charges. Although exotic nonlinear excitations have been theoretically proposed in the superfluid ³He-A phase and spinor Bose–Einstein condensates, they have not been experimentally observed and their stability has not been investigated. Here we demonstrate the presence of a singular skyrmion that goes beyond the framework of topology in a ferromagnetic superfluid. These skyrmions emerge from anomalous symmetry-breaking associated with an eccentric spin singularity and carry half the elementary charge—a feature that distinguishes them from conventional skyrmions and merons. We realize the universal regime of the quantum Kelvin–Helmholtz instability, and we identify the unconventional fractional skyrmions produced by emission from a magnetic domain wall and the spontaneous splitting of an integer skyrmion with spin singularities. The singular skyrmions are stable even after 2 s of hold time. Our results confirm the universality between classical and quantum Kelvin–Helmholtz instabilities and broaden our understanding of complex nonlinear dynamics for a non-trivial texture in topological quantum systems.</p>