By 
Good (for hyperkinesis) to the last drop –Science News, July 14, 1973
[Hyperactive] children are sometimes given amphetamines to calm them down.… [A researcher] took 11 such children off medication and gave them one cup of coffee at breakfast and lunch…. Teachers and parents rated the children as less hyperactive during the three-week period they were getting coffee instead of amphetamines.
Update
Attention-deficit/ hyperactivity disorder affects about 6 million U.S. children. Most medical professionals recommend managing symptoms with talk therapy and stimulant medications. For people with ADHD, stimulants boost levels of dopamine and norepinephrine in the brain to improve impulse control, focus and working memory (SN: 3/31/17). Caffeine also boosts dopamine, but evidence that coffee or other caffeinated foods relieve ADHD symptoms is sparse and inconsistent.
A few studies in children with ADHD hint that caffeine improves attention and impulse control compared with no treatment, while other studies suggest the opposite. Pediatricians generally advise against giving kids caffeine due to its effect on sleep.
