Autism spectrum disorder (ASD) poses a complex challenge to researchers and practitioners, with its multifaceted etiology and varied manifestations. Timely intervention is critical in enhancing the developmental outcomes of individuals with ASD. This paper underscores the paramount significance of early detection and diagnosis as a pivotal precursor to effective intervention. To this end, integrating advanced technological tools, specifically eye-tracking technology and deep learning algorithms, is investigated for its potential to discriminate between children with ASD and their typically developing (TD) peers. By employing these methods, the research aims to contribute to refining early detection strategies and support mechanisms. This study introduces innovative deep learning models grounded in convolutional neural network (CNN) and recurrent neural network (RNN) architectures, employing an eye-tracking dataset for training. Of note, performance outcomes have been realised, with the bidirectional long short-term memory (BiLSTM) achieving an accuracy of 96.44%, the gated recurrent unit (GRU) attaining 97.49%, the CNN-LSTM hybridising to 97.94%, and the LSTM achieving the most remarkable accuracy result of 98.33%. These outcomes underscore the efficacy of the applied methodologies and the potential of advanced computational frameworks in achieving substantial accuracy levels in ASD detection and classification.