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Automatic modulation recognition (AMR) is used in various domains—from general-purpose communication to many military applications—thanks to the growing popularity of the Internet of Things (IoT) and related communication technologies. In this research article, we propose an innovative idea of combining the classical mathematical technique of computing linear combinations (LCs) of cumulants with a genetic algorithm (GA) to create super-cumulants. These super-cumulants are further used to classify five digital modulation schemes on fading channels using the K-nearest neighbor (KNN). Our proposed classifier significantly improves the percentage recognition accuracy at lower SNRs when using smaller sample sizes. A comparison with existing techniques manifests the supremacy of our proposed classifier.