This paper proposes a method to create and manipulate higher-order topological states using alternagnets. Alternagnets, which exhibit unique spin-polarization in both real and reciprocal space and null magnetization, are combined with a two-dimensional topological insulator to generate higher-order topological states. By adjusting the direction of the Néel vector in the alternagnet, the topological corner states can be manipulated. The study demonstrates the feasibility of this approach through first-principles calculations, using a 2D topological insulator bismuthene on an alternagnet MnF₂. The results show that the system can exhibit non-Abelian braiding of Dirac corner fermions. The research also discusses the experimental implementation and detection of these topological corner states, highlighting the potential for applications in quantum information processing. The study provides a new platform for realizing non-Abelian statistics using topological corner states. The paper also includes a detailed supplementary material that covers the edge theory, mirror-graded winding number, and other computational details.This paper proposes a method to create and manipulate higher-order topological states using alternagnets. Alternagnets, which exhibit unique spin-polarization in both real and reciprocal space and null magnetization, are combined with a two-dimensional topological insulator to generate higher-order topological states. By adjusting the direction of the Néel vector in the alternagnet, the topological corner states can be manipulated. The study demonstrates the feasibility of this approach through first-principles calculations, using a 2D topological insulator bismuthene on an alternagnet MnF₂. The results show that the system can exhibit non-Abelian braiding of Dirac corner fermions. The research also discusses the experimental implementation and detection of these topological corner states, highlighting the potential for applications in quantum information processing. The study provides a new platform for realizing non-Abelian statistics using topological corner states. The paper also includes a detailed supplementary material that covers the edge theory, mirror-graded winding number, and other computational details.