Background Emerging evidence suggests that cognitive impairment cuts across traditional psychiatric diagnoses and may reflect a shared underlying cognitive liability. We examined whether a general cognitive factor (gFc) accounts for transdiagnostic deficits across schizophrenia (SZ), bipolar disorder (BD), obsessive-compulsive disorder (OCD) and substance use disorder (SUD). Methods A total of 797 individuals [544 affected and 253 healthy controls (HC)] completed a standardized cognitive battery. Bifactor confirmatory factor analysis was used to derive general cognitive factor (gFc) and domain-specific impairments (cognitive flexibility, working memory, new learning and social cognition). Model fit supported the bifactor structure. Linear mixed-effect models, with family as random effect, and demographic variables as fixed effect evaluated transdiagnostic and diagnosis specific impairments. Results The gFc was significantly reduced across all diagnoses groups relative to HC, [B(SE): BD -0.49 (0.07), OCD -0.21 (0.07), SUD -0.43(0.08), SZ -0.76 (0.08), all p < 0.001]; verbal learning showed additional diagnosis-specific deficits, most pronounced in SZ [B (SE):0.59 (0.09)] and BD[B(SE):0.48 (0.09)], both p < 0.001. Conclusion A single gFc accounts for substantial cognitive dysfunction across major psychiatric disorders, while verbal-learning impairment appears diagnosis-specific. These findings support a dimensional architecture of cognition in psychiatry and identify gFc as a promising transdiagnostic target for clinical and mechanistic research.