In many animals, including humans, interactions with caring parents can have long-lasting effects on offspring sensitivity to stressors. However, whether these parental effects impact offspring fitness in nature is often unclear. In addition, despite evidence that maternal care can influence offspring behaviour via epigenetic alterations to the genome, it remains unclear whether paternal care has similar effects. Here, we show in three-spined sticklebacks, a fish in which fathers are the sole provider of offspring care, that the direct care provided by fathers affects offspring anxiety and the potential for epigenetic alterations to the offspring genome. We find that families are differentially vulnerable to early stress and fathers can compensate for this differential sensitivity with the quality of their care. This variation in paternal care is also linked to the expression in offspring brains of a DNA methyltransferase (Dnmt3a) responsible for de novo methylation. We show that these paternal effects are potentially adaptive and anxious offspring are unlikely to survive an encounter with a predator. By supplying offspring care, fathers reduce offspring anxiety thereby increasing the survival of their offspring—not in the traditional sense through resource provisioning but through an epigenetic effect on offspring behavioural development.