We investigate the magnon band topology and transverse transport in an antiferromagnetic $\alpha \text{−}{T}_3$ lattice with Dzyaloshinskii-Moriya interaction (DMI) and single-ion anisotropy. Using linear spin-wave theory, we show that the lattice geometry, controlled by the parameter $\alpha$, together with the DMI, drives a topological phase transition when the two lower magnon bands become degenerate at the $\mathbf{K}$ point of the first Brillouin zone. The transition occurs along the critical line $D/J_1=(1-\alpha )/2\sqrt{3}$, separating a trivial phase with Chern numbers $C=(0,0,0)$ from a nontrivial phase with $C=(-2,2,0)$. This topological transition is directly manifested in the transverse transport of magnons. At $k_{B}T=J_1$, the magnon spin Nernst and thermal Hall coefficients increase by up to a factor of 3 and 8, respectively, when the system transitions from the trivial to the topological phase, driven by the large Berry curvature near the $\mathbf{K}$ point. We also examine the effect of sublattice inequivalence and demonstrate that the essential connection between nontrivial topology and enhanced transport remains robust. Our results establish the $\alpha \text{−}{T}_3$ antiferromagnet as a tunable platform for topological magnonics and provide clear theoretical predictions for experimental detection.

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• Antiferromagnetism
• Exchange interaction
• Antiferromagnets
• Heisenberg model
• Holstein-Primakoff method
• Spin wave theory