To what extent are genetic effects on children’s education, occupational standing, and income shaped by their parents’ socioeconomic characteristics? Does the impact vary over their children’s early life course, and are there differences across the social strata? We studied these research questions with Finnish register-based data on 6,542 pairs of twins born from 1975 to 1986. We applied the classical twin design to estimate the relative importance of genes. As outcomes, we compared education, occupation, and income in early adulthood. We found that shared environment influences were negligible in all cases. Notably, the proportion of genetic effects explained by parental characteristics mattered most for education and for occupation only because they were associated with their children’s education—but not for income. We did not find any variation across their early life course; however, we found that genetic influences were stronger among the advantaged families for income and education. Thus, gene-environment interactions (GxE) operate differently for different status-related characteristics. For the unique environment, the pattern was consistent across outcomes as the effect was greater among the advantaged families. Stratification scholars should therefore emphasize the importance of the unique environment as one of the drivers of the intergenerational transmission of social inequalities.