My nephew who's 7 years old takes Melatonin and his doctor said to start giving him 3 mg of Melatonin at first to see if it would be enough to get him to sleep and it does.
The doctor said though if 3 mg of Melatonin wasn't enough then to up the dose to 6 mg but not to go higher than that at his age.
For older children past age 10 and up then you could give the child or teen a little more which could be from 15 to 25 mg of Melatonin to help them sleep.