Abstract: We report characteristic vortex configurations in s + id superconductors with time-reversal symmetry breaking, exposed to magnetic field. A vortex in the s + id state tends to have an opposite phase winding between s- and d-wave condensates. We find that this peculiar feature together with the competition between s- and d-wave symmetry results in three distinct classes of vortical configurations. When either s or d condensate absolutely dominates, vortices form a conventional lattice. However, when one condensate is relatively dominant, vortices organize in chains that exhibit skyrmionic character, separating the chiral components of the s +/- id order parameter into domains within and outside the chain. Such skyrmionic chains are found stable even at high magnetic field. When s and d condensates have comparable strength, vortices split cores in two chiral components to form full-fledged skyrmions, i.e., coreless topological structures with an integer topological charge, organized in a lattice. We provide characteristic magnetic field distributions of all states, enabling their identification in, e.g., scanning Hall probe and scanning SQUID experiments. These unique vortex states are relevant for high-T-c cuprate and iron-based superconductors, where the relative strength of competing pairing symmetries is expected to be tuned by temperature and/or doping level, and can help distinguish s + is and s + id superconducting phases.