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In the framework of the microscopic Bogoliubov-de Gennes theory, we study the topological defect states in mesoscopic superconducting square systems with spin correlations. The dominant spin-triplet (px ± ipy)-wave pairing symmetry of order parameters can be realized by choosing appropriate band parameters. At zero external magnetic field, the single-domainwall state tends to emerge as the ground state of the system. When the magnetic field is applied, there exist field-driven phase transitions among three types of (anti)vortex patterns for the vortexfree ground state. With increasing field, a large number of coreless single-skyrmionic states with different topological charges can appear as the ground states. In particular, a novel chiral domainwall ground state carrying fractional total flux quanta can take place, accompanied by an unclosed half-quantum-vortex chain in the phase difference profile. Several unique metastable states are also revealed in the strong flux range in the present system.

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