Even-layer topological antiferromagnetic thin films such as MnBi₂Te₄ exhibit an unconventional layer Hall effect (LHE) arising from a layer-locked Berry curvature. This effect manifests as a layer-polarized anomalous Hall effect that can be controlled by a vertical displacement field. However, achieving a quantized version of the LHE remains experimentally challenging. In this work, we propose that moiré engineering, using an electrostatic superlattice potential from control layers, can realize the quantum layer Hall effect (QLHE). Specifically, by placing moiré control layers in close proximity to the surfaces of a MnBi₂Te₄ thin film without breaking PT symmetry, the resulting system exhibits a vanishing net Hall conductance but a quantized layer Hall conductance of e²/h. A weak gate electric field then breaks PT symmetry and drives the system into a layer-polarized quantum anomalous Hall (QAH) phase. Furthermore, when a single control layer is introduced on only one surface, the layer-polarized QAH emerges even in the absence of an external electric field. We identify the microscopic origin of the QLHE as an emergent layer-U(1) gauge field generated by the scalar moiré potential, which in turn produces opposite periodic pseudomagnetic fields on the top and bottom layers. Our work provides a feasible pathway toward realizing the QLHE in antiferromagnetic thin films.