The Nocturnal Frontal Lobe Epilepsy (NFLE) is a form of epilepsy in which seizures occur predominantly during sleep. In other forms of epilepsy, the commonly used clinical approach mainly involves manual inspection of encephalography (EEG) signals, a laborious and time-consuming process which often requires the contribution of more than one experienced neurologist. In the last decades, numerous approaches to automate this detection have been proposed and, more recently, machine learning has shown very promising performance. In this paper, an original Convolutional Neural Network (CNN) architecture is proposed to develop patient-specific seizure detection models for three patients affected by NFLE. The performances, in terms of accuracy, sensitivity, and specificity, exceed by several percentage points those in the most recent literature. The capability of the patient-specific models has been also tested to compare the obtained seizure onset times with those provided by the neurologists, with encouraging results. Moreover, the same CNN architecture has been used to develop a cross-patient seizure detection system, resorting to the transfer-learning paradigm. Starting from a patient-specific model, few data from a new patient are enough to customize his model. This contribution aims to alleviate the task of neurologists, who may have a robust indication to corroborate their clinical conclusions.