The idea that exposure to high amounts of sugar makes children more prone to develop attention deficit disorder or worsens symptoms in those who have attention deficit disorder is a very common popular notion. However, there is no evidence to support this idea.
In one very interesting study, children were all given an artificial (not sugar) sweetener without the parents knowing whether the sweetener was real or artificial sugar. However, in the parents who thought their children were taking real sugar, there was a much higher rate of reporting symptoms of hyperactivity. However, there was no objective evidence of hyperactivity. This supports the idea that we associate hyperactivity and sugar culturally, but this is simply a misconception.
Of course, there are many other reason to limit the amount of sugar in a child's diet. First and foremost, unhealthy eating, including taking in large amounts of sugar, predisposes to obesity, diabetes, and other major medical problems. Second, large amounts of sugar are harmful to the teeth. So we should all work on supplying children with healthy, balanced diets and limiting their intake of sugar, but not in order to prevent hyperactivity.
If you have more questions about attention deficit disorder, talk to your child's pediatrician