Some damages to the cerebral cortex, especially neonatal seizures, are detected using electroencephalogram (EEG) in the neonatal intensive care unit (NICU). Given the non-stationary and multicomponent nature of the EEG and lack of clinical symptoms of seizures in neonates, the EEG interpretation is complicated, time-consuming and requires specialized staff. Therefore, development of automatic methods for neonatal seizure detection is crucial. Studies demonstrate that the time-frequency methods are superior to methods in either the time or the frequency domain. Additionally, adaptive time-frequency methods yield better results, compared to their counterparts. Among the adaptive time-frequency transforms (ATFTs), the adaptive Fourier synchrosqueezing transform (AFSST) has led to promising results. The AFSST solely encompasses frequency reassignment, thereby being more suitable for representing slowly varying components. Conversely, the time-reassigned Fourier synchrosqueezing transform is more convenient for fast-changing components. Neonatal seizures comprise various component types. Hence, it is necessary to employ a TFT that is capable of representing them sharply and accurately. This study aims at improvement of neonatal seizure detection using an ATFT and time-frequency features. Thus, for the first time, the time-reassigned adaptive Fourier synchrosqueezing transform with globally optimal window length (TAFSSTOL) is applied on neonatal seizures, along with using the set-based integer-coded fuzzy granular evolutionary algorithm (SIFE) and Bayesian optimization for selecting the features and classifiers, respectively. Furthermore, time and frequency domain features are extracted. Some features have never been utilized in the literature. For time-frequency features, AFSST is also used. The time-frequency features that were extracted from TAFSSTOL led to the best classification performance (accuracy: 100%, sensitivity: 100%, specificity: 100%, precision: 100%, negative predictive value: 100%, F1 score: 100%, Matthew’s correlation coefficient: 100%, Cohen’s κ value: 100%, area under the receiver operating characteristic curve: 1). Thus, the TAFSSTOL is apt for various components separation and neonatal seizure detection.