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There are several knot invariants in the literature that are defined usingsingular instantons. Such invariants provide strong tools to study the knotgroup and give topological applications. For instance, it gives powerful toolsto study the topology of knots in terms of representations of fundamentalgroups. In particular, it is shown that any traceless representation of thetorus knot group can be extended to any concordance from the torus knot toanother knot. Daemi and Scaduto proposed a generalization that is related to aversion of the Slice-Ribbon conjecture to torus knots. The results of thispaper provide further evidence towards the positive answer to this question.The method is a generalization of Daemi-Scaduto's equivariant singularinstanton Floer theory following Echeverria's earlier work. Moreover, theirreducible singular instanton homology of torus knots for all but finitelymany rational holonomy parameters are determined as $\mathbb{Z}/4$-gradedabelian groups.

Instanton knot invariants with rational holonomy parameters and an application for torus knot groups