The idea that the age of fathers (i.e. the father's age at conception of their children) might affect the ongoing physical and psychological health of their children goes back to 1912.

Various effects have been studied, including the probability of the children developing cancers, various genetic syndromes and psychological problems such asSchizophreniaplugin-autotooltip__plain plugin-autotooltip_bigSchizophrenia

"Schizophrenia is a mental disorder characterized by abnormal social behavior and failure to understand what is real. Common symptoms include false beliefs, unclear or confused thinking, auditory and visual hallucinations, reduced social engagement and emotional expression, and a lack of motivation."andAutismplugin-autotooltip__plain plugin-autotooltip_bigAutism

Autism is a developmental disorder characterized by difficulties with social interaction and communication, and by restricted and repetitive behaviour. The causes of autism are unknown, though it's likely that there is a strong genetic component. Current theory suggests a complex disorder which has core aspects that have distinct causes and often co-occur..

It's been determined that If there are associations, the effects are generally very small.

The mechanism is presumed to be due to 'faulty' DNA coding, but how this works in practice, especially with the psychological problems, is unclear.

There are currently four main theories which attempt to explain how the mechanism might be operating - see Wikipedia

For a current overview of possible psychological associations, see : Am J Med Genet B Neuropsychiatr Genet. 2017 Apr; 174(3): 202–213