L-Theanine stimulates the brain into releasing a calming hormone into the body. This helps children with ADHD because it's a natural stimulant that doesn't have the addictive quality of Ritalin.
L-Theanine is an amino acid that promotes relaxation by promoting alpha brain wave production that is useful for promoting focus, calm and attentiveness which could be helpful with adhd.
L-theanine is mainly good for anxiety. It helps relax the nervous system. It may be useful in ADHD by calming down the child's overactivity and hyperness.
I don't know about ADHD specifically, but numerous peer-reviewed scientific studies have shown L-Theanine has had modest but consistent effects in lowerinf mental stress and improving mood.