The parity anomaly of a single massless Dirac fermion in $(2+1)$ dimensions produces a half-quantized Hall conductance, a phenomenon recently confirmed on the surface of three-dimensional (3D) ${\mathbb{Z}}_2$ topological insulators. Whether and how this anomaly generalizes to 3D topological phases carrying an integer winding number $W$ has remained an open question. Here, we address this problem for 3D chiral topological systems in the Altland-Zirnbauer symmetry classes AIII and DIII. By constructing minimal lattice models, we show that the winding number fixes the net chirality of the boundary Dirac or Majorana cones. By introducing a time-reversal-breaking surface mass to provide the necessary high-energy regularization, we explicitly expose their intrinsic parity anomaly. Through a layer-resolved Chern-number analysis, we establish a macroscopic topological magnitude law, $|{\mathcal{C}}_{\mathrm{surf}}|=|W|/2$, revealing that the shared chirality enforces a constructive accumulation of the fractional topological charges. We further demonstrate that this amplified anomaly coefficient is unambiguously readable in transport: a four-terminal setup in class AIII yields a quantized transmission asymmetry $\left|\mathrm{\Delta }T\right|=\left|W\right|/2$, while a six-terminal thermal Hall measurement in class DIII topological superconductors gives $|{\kappa }_{xy}^{\mathrm{surf}}|=|W|/4{\kappa }_0$. Notably, this thermal signature remains strictly robust against 3D Anderson disorder. Our results establish that the bulk winding number universally controls the macroscopic surface parity-anomaly coefficient in 3D chiral topological phases, providing concrete transport protocols for its detection in artificial metamaterial platforms and topological superconductor candidates.

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• Surface states
• Topological insulators
• Transport phenomena
• Chiral symmetry
• Nonequilibrium Green's function