Vortex and skyrmionic patterns in chiral p-wave superconducting systems

•The coreless single or multiple skyrmionic structures and several types of the skyrmion-vortex coexisting modes can remain stable in bulk p-wave superconducting systems.•The multiskyrmionic patterns containing several separated skyrmionic chains emerge at an appropriate flux, accompanied with half-quantum vortex-antivortex pairs in one component of the order parameter.•Complex skyrmionic states with the topological charge Q > 2 can also take place when the external magnetic flux becomes stronger.