The aim of this study was to examine associations between selected sociodemographic, socioeconomic, and health characteristics and the rates of fatherhood in different age groups. We investigated rates between 2011 and 2015 in a population-based register study including all men born from 1945 to 1995 residing in Denmark in 2011. The study population consisted of 1,867,108 men who fathered 268,612 children during the follow-up. The associations were quantified as incidence rate ratios using Poisson regression. Young men had higher rates of fathering a child if they lived outside the Capital Region, had a relatively high income, were previously diagnosed with cardiovascular disease, psychoactive substance abuse, personality disorders, schizophrenia or behavioural and emotional disorders. Men of advanced age had higher rates of fathering a child when born outside Denmark, living in the Capital Region, were in the lower or upper 10th percentile income group, were self-employed or unemployed or previously diagnosed with depression. Men of advanced age had lower rates of fathering a child if previously diagnosed with somatic diseases, psychoactive substance abuse or mental retardation. The findings highlight the importance of consideration of various sociodemographic, socioeconomic, and health characteristics when studying associations between paternal age and offspring health.