Attention-Deficit/Hyperactivity Disorder (ADHD) is a complex neurodevelopmental condition characterized by persistent challenges in attention, hyperactivity, and impulsivity, significantly impacting daily functioning and developmental trajectories. The traditional ADHD diagnostic process typically involves comprehensive assessments conducted by healthcare professionals, such as psychologists, psychiatrists, or pediatricians. These assessments rely heavily on subjective observations and reports from various sources. However, this approach is time-consuming, labor-intensive, and often requires multiple appointments which makes it a resource-intensive process. To address this issue, I propose an unsupervised learning-based gaze estimation system for the screening of ADHD. The proposed system takes eye images as input and generates gaze vectors which indicate the individual's current focal point. By aggregating these gaze vectors over a specific time series, the system can identify abnormalities in the gaze patterns which facilitate the early screening of ADHD. Comprehensive experiments have shown the superiority of the proposed system over previous methods. The experimental results also confirm the feasibility of utilizing the proposed method as a biometric for screening ADHD.