You'll find it easier to answer this question if you refine it more carefully. "Mental illness" is far too broad a category, and the answer will vary by diagnosis. For example, schizophrenia is thought to have a genetic component and generally has onset in late adolescence or early adulthood. Autism is diagnosed early in childhood and not thought to be hereditary. Most research will be focused on the specific disorder. I'll send some articles in additional answers.
One article that looks at age of onset is
Age of onset of mental disorders: A review of recent literature
Ronald C. Kessler, PhD, G. Paul Amminger, MD, Sergio Aguilar‐Gaxiola, MD, PhD, Jordi Alonso, MD, Sing Lee, MD, and T. Bedirhan Ustun, MD
Curr Opin Psychiatry. 2007 Jul; 20(4): 359–364.
doi: 10.1097/YCO.0b013e32816ebc8c
Link at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1925038/
A more recent article
Adult mental health disorders and their age at onset
P. B. Jones
The British Journal of Psychiatry Jan 2013, 202 (s54) s5-s10; DOI: 10.1192/bjp.bp.112.119164
Link at http://bjp.rcpsych.org/content/202/s54/s5
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