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The purpose of this study was to explore the association of cognition with hazardous drinking Polygenic Scores (PGS) in 2649 schizophrenia, 558 schizoaffective disorder, and 1125 bipolar disorder patients in Finland. Hazardous drinking PGS was computed using the LDPred program. Participants performed two computerized tasks from the Cambridge Automated Neuropsychological Test Battery (CANTAB) on a tablet computer: the 5-choice serial reaction time task, or Reaction Time (RT) test, and the Paired Associative Learning (PAL) test. The association between hazardous drinking PGS and cognition was measured using four cognition variables. Log-linear regression was used in Reaction Time (RT) assessment, and logistic regression was used in PAL assessment. All analyses were conducted separately for males and females. After adjustment of age, age of onset, education, household pattern, and depressive symptoms, hazardous drinking PGS was not associated with reaction time or visual memory in male or female patients with schizophrenia, schizoaffective, and bipolar disorder.