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 probabliity of the children developing cancers, various genetic syndromes and psychological problems such asand .
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, see Wikipedia
For a current overview of possible psychological associations, see : Am J Med Genet B Neuropsychiatr Genet. 2017 Apr; 174(3): 202–213
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