Cognitive impairment is a core feature of many neuropsychiatric disorders and a major determinant of quality of life, yet it remains poorly treated by existing psychotropic medications. Genetic studies have revealed substantial overlap between risk factors for psychiatric disorders and cognitive function, but most have relied on broad, heterogeneous measures of cognition rather than distinct cognitive domains. To refine these relationships, we employed a network-based genomic approach to identify which cognitive domains exhibit the most direct genetic links to psychiatric diagnoses. Using genome-wide association study (GWAS) data from the UK Biobank, we constructed a network of conditional genetic correlations across cognitive tests reflecting processing speed, executive function, working memory, reasoning, and visual memory. This refined which cognitive domains still display evidence of genetic overlap after accounting for all other cognitive traits tested. Integration of schizophrenia into the cognitive genetic network demonstrated that a measure of executive function—indexed by the trail making test (TM2)—is the cognitive domain with the strongest genetic link to schizophrenia after conditioning on all other features. We further examined this relationship using two complementary bivariate approaches: Local Analysis of [co]Variant Association (LAVA), which quantifies local genetic correlation, and pairwise GWAS, which classifies loci as shared or trait-specific. LAVA identified 22 genomic regions with significant (FDR < 0.05) local genetic correlation between TM2 and schizophrenia, while pairwise GWAS identified that five of these regions are likely driven by a shared causal variant. Gene-based mapping of these regions highlighted plausible effector genes that influence both executive function and schizophrenia, including SLC39A8, linked to brain metal ion transport and glycosylation, and TSNARE1, involved in synaptic vesicle trafficking. Work is ongoing to further utilise these data to identify potential nootropic therapeutic targets for schizophrenia and other psychiatric diagnoses where cognitive deficits remain poorly treated.