The precise mathematical description of gaze patterns is still an unsettled matter of debate. This can, consequently, affect the analysis of this type of data in its practical applications. In this scope, we show evidence that a Lévy-flight description of eye-gaze trajectories is not only appropriate but its scale invariant properties are remarkably useful to assist in diagnosing children with Attention Deficit and Hyperactivity Disorder (ADHD), alongside with the usual cognitive tests. Using this picture, we find that the distribution of the characteristic exponent of Lévy-flights statistically is different in children with ADHD. Furthermore, we observe that these children deviate from a strategy that is considered optimal for searching processes, in contrast to non-ADHD children. We focus on the case where both eye-tracking data and data from a cognitive test are present and show that the study of gaze patterns in children with ADHD can help in identifying this condition. Since eye-tracking data can be gathered during cognitive tests without needing extra time-consuming specific tasks, we argue that it is in prime position to provide assistance in the arduous task of ADHD diagnosing.