A limited number of electroencephalography (EEG) channels are useful for neonatal sleep classification, particularly in the Internet of Medical Things (IoMT) field, where compact and lightweight devices are essential to monitoring health effectively. A streamlined and cost-effective IoMT solution can be achieved by utilizing fewer EEG channels, thereby reducing data transmission and device processing requirements. Using only two channels of an EEG device, this study presents a binary and multistage classification of neonatal sleep. The binary classification (sleep vs awake) achieved an accuracy of 87.56%, and a Cohen’s kappa of 74.13%. The quiet sleep ( QS ) detection accuracy was 95.63%, with a Cohen’s kappa of 83.87%. For the three-stage classification, accuracy was 83.72%, and Cohen’s kappa was 69.73%. With only two channels, these are the highest performance parameters. The focus is on the fusion of features extracted through flexible analytical wavelet transform (FAWT) & discrete wavelet transform (DWT), ensemble-based voting models, and fewer channels. To feed crucial features into the ensemble-based voting model, feature importance, feature selection, and validation mechanisms were used. To design the voting classifier, several machine learning models were used, compared, and optimized. With SelectKBest feature selection, the proposed methodology was found to be the most effective. By using only two channels, this study shows the practicality of classifying neonatal sleep stages.