Children of fathers with antisocial personality disorder (ASPD) are at risk for developing delinquency, and both biological and environmental mechanisms contribute. In this study, we test parasympathetic nervous system (PNS) function as a vulnerability/sensitivity attribute in predicting intergenerational associations between fathers' antisociality and children's delinquency scores. We followed 207 children (ages 8–12 years at intake; 139 boys) across three annual assessments. Fathers' antisociality was measured via maternal reports on the Family Interview for Genetic Studies (FIGS). At Year 1, children's resting respiratory sinus arrhythmia (RSA) was measured. At Years 1, 2, and 3, child delinquent behaviors were assessed using the delinquency subscale of the Youth Self‐Report. At age 8, boys' delinquency scores were associated weakly with paternal antisocial behaviors. However, boys' delinquency scores increased steeply thereafter specifically for those who had fathers with higher antisocial symptoms. In addition, associations between delinquency and paternal antisociality were largest for boys with higher resting RSA. For girls, growth in delinquency was unrelated to both father antisociality and resting RSA. These findings (a) suggest moderating effects of children's age, sex, and PNS function on associations between father antisocial behavior and offspring delinquency; and (b) provide insights into differential vulnerability among children of fathers with ASPD.