The Cyclic Alternating Pattern (CAP) can be considered a physiological marker of sleep instability. The CAP can examine various sleep-related disorders. Certain short events (A and B phases) manifest related to a specific physiological process or pathology during non-rapid eye movement (NREM) sleep. These phases unexpectedly modify EEG oscillations; hence, manual detection is challenging. Therefore, it is highly desirable to have an automated system for detecting the A-phases (AP).Deep convolution neural networks (CNN) have shown high performance in various healthcare applications. A variant of the deep neural network called the Wavelet Scattering Network (WSN) has been used to overcome the specific limitations of CNN, such as the need for a large amount of data to train the model. WSN is an optimized network that can learn features that help discriminate patterns hidden inside signals. Also, WSNs are invariant to local perturbations, making the network significantly more reliable and effective. It can also help improve performance on tasks where data is minimal. In this study, we proposed a novel WSN-based CAPSCNet to automatically detect AP using EEG signals. Seven dataset variants of cyclic alternating pattern (CAP) sleep cohort is employed for this study. Two electroencephalograms (EEG) derivations, namely: C4-A1 and F4-C4, are used to develop the CAPSCNet. The model is examined using healthy subjects and patients tormented by six different sleep disorders, namely: sleep-disordered breathing (SDB), insomnia, nocturnal frontal lobe epilepsy (NFLE), narcolepsy, periodic leg movement disorder (PLM) and rapid eye movement behavior disorder (RBD) subjects. Several different machine-learning algorithms were used to classify the features obtained from the WSN. The proposed CAPSCNet has achieved the highest average classification accuracy of 83.4% using a trilayered neural network classifier for the healthy data variant. The proposed CAPSCNet is efficient and computationally faster.