The purpose of this study was to explore the association between cognition and hazardous drinking and alcohol use disorder in schizophrenia and schizoaffective disorder. Cognition is more or less compromised in schizophrenia, and schizoaffective disorder and alcohol use might aggravate this phenomenon. The study population included 3362 individuals from Finland with diagnoses of schizophrenia or schizoaffective disorder. Hazardous drinking was screened with the AUDIT-C (Alcohol Use Disorders Identification Test for Consumption) screening tool. Alcohol use disorder (AUD) diagnoses were obtained from national registrar data. Participants performed two computerized tasks from the Cambridge Automated Neuropsychological Test Battery (CANTAB) on a tablet computer: The Five-Choice Serial Reaction Time Task (5-CSRTT) or the reaction time (RT) test and the Paired Associative Learning (PAL) test. The association between alcohol use and the RT and PAL tests was analyzed with log-linear regression and logistic regression, respectively. After adjustment for age, education, housing status, and the age at which the respondents had their first psychotic episodes, hazardous drinking was associated with a lower median RT in females and less variable RT in males, while AUD was associated with a poorer PAL test performance in terms of the total errors adjusted scores (TEASs) in females. Our findings of positive associations between alcohol and cognition in schizophrenia and schizoaffective disorder are unique.