Functional connectivity (FC) as derived from fMRI has emerged as a pivotal tool in elucidating the intricacies of various psychiatric disorders and in delineating the neural pathways that underpin cognitive and behavioral dynamics inherent to the human brain. While Graph Neural Networks (GNNs) offer a structured approach to represent neuroimaging data, they are limited by their need for a predefined graph structure to depict associations between brain regions, a detail not solely provided by FCs. To bridge this gap, we introduce the Gated Graph Transformer (GGT) framework, designed to predict cognitive metrics based on FCs. Empirical validation on the Philadelphia Neurodevelopmental Cohort (PNC) underscores the superior predictive prowess of our model, further accentuating its potential in identifying pivotal neural connectivities that correlate with human cognitive processes.