Abstract Motivated by a recent experiment on high-temperature superconductors [Nature 615, 405 (2023)], we perform a theoretical study to distinguish the nature of the topological spin texture in the superconducting phase of an underdoped cuperate. We propose a phenomenological tight-binding model of electrons with spin-singlet pairing hopping in the background of topological spin texture on the square lattice. Two types of topological spin texture relevant to the experiment are considered, i.e. Bloch Skyrmion and sinusoidal vortex, and the mean-field theory is employed. We discover an emergent $d_{xy}$-wave component in imaginary part of gap function for Skyrmion, but there is not for vortex. For Skyrmion, each coherent peak in the local density of states splits into two spatial uniform peaks, while for vortex, it splits into two spatial modulated peaks. Our study reveals the qualitatively different consequences of two types of topological spin texture, and can be possibly detected in the further STM expriment.
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