Inducing superconducting correlations in quantum anomalous Hall (QAH) states offers a promising route to realize topological superconductivity with chiral Majorana edge modes. However, the definitive identification of these modes is challenging. Here we propose detecting superconducting chiral edge modes via the probability distribution of the resistance, or equivalently the charge transmission of QAH-superconductor heterojunctions. Remarkably, the distribution for coherent edge exhibits distinct characteristics for different topological superconducting phases in sufficiently long junctions, and this difference remains robust against weak decoherence. These findings provide insights into transport phenomena beyond the clean limit and highlight the resistance distribution as a compelling signature for distinguishing topological superconducting phases.