Objective: Parental severe mental illness (SMI) increases the lifetime risk of mental and pediatric disorders in the offspring but little is known about specific disorders during early childhood. The primary aim was to investigate the incidence of mental and pediatric disorders among children 0–6 years old exposed to parental SMI, and secondarily to investigate the distribution of disorders on specific child age. Methods: A nationwide, register-based cohort study of 1,477,185 children born in Denmark between 1994.01.01 and 2016.12.31. Incidence rate ratios were calculated using Poisson regression analysis for any and specific mental and pediatric disorders. Results: IRR for any psychiatric disorder was elevated by a factor 2–5 among SMI offspring. Maternal schizophrenia resulted in the highest IRR = 5.23 (4.80–5.69) of any child psychiatric disorder. The risk of anxiety/OCD and attachment disorder among offspring exposed to parental, and in particular maternal, SMI was markedly raised with IRRs for anxiety/OCD between 7.59 and 17.02 and attachment disorders between 6.26 and 15.40. IRRs of mental disorders were highest at age 0–1 year and declined with age. IRR for any pediatric disorder was also elevated with IRRs between 1.01 and 1.28. Disorders of the digestive system and ill-defined symptoms were associated with the highest IRRs. Maternal (vs. paternal) SMI was associated with higher IRRs. IRRs declined slightly with child age. Conclusion: Children exposed to parental SMI are at increased risk of mental and pediatric disorders during early childhood, particularly anxiety/OCD and attachment disorders. If associations are estimates of a modifiable causal relationship, our results indicate a need for early intervention to promote mental and pediatric health among SMI offspring.