There have been several proposals for platforms supporting topological superconductivity in high-temperature superconductors, in order to make use of the larger superconducting gap and the expected robustness of Majorana zero modes towards perturbations. In particular, the iron-based materials offer relatively large Tc and nodeless energy gaps. In addition, atomically flat surfaces enable the engineering of defect structures and the subsequent measurement of spectroscopic properties to reveal topological aspects. From a theory perspective, a materialsspecific description is challenging due to the correlated nature of the materials and complications arising from the multiband nature of the electronic structure. Here we include both aspects in realistic interacting models, and find that the correlations themselves can lead to local magnetic order close to linear potential scattering defects at the surface of the superconductor. Using a self-consistent Bogoliubov-de Gennes framework in a real-space setup using a prototype electronic structure, we allow for arbitrary magnetic orders and show how a topological superconducting state emerges. The calculation of the topological invariant and the topological gap allows us to map out the phase diagram for the case of a linear chain of potential scatterers. While intrinsic spin-orbit coupling is not needed to enter the topological state in the presence of spin-spiral states, it enlarges the topological phase. We discuss the interplay of a triplet component of the superconducting order parameter and the spin spiral leading effectively to extended spin-orbit coupling terms, and connect our results to experimental efforts on the Fe(Se,Te) system.