IMO, the best cognitive enhancers for children would be: sleep, healthy diet, exercise, and social interaction. There was also a study done that kids who were given music lessons showing that musical training at an early age adds an extra 5.1-7.6 IQ points. The highest IQ boost was from voice lessons, followed by keyboard/piano. Also, teaching a second language at an early age would provide many benefits, not just cognitive.
Ok, I'm going to say this one time and fairly certain others agree with it. You should not be giving children nootropics, period with the exception perhaps being piracetam for down syndrome and even that is a bit iffy
For this matter it's dangerous taking advice from people in here as many don't know what they are talking about
Consult with your doctor/psychiatrist and put him on a good diet with quality protein, omega 3's and cut down on high glycemic carbohydrates (sugar), exercise daily, socialize (if possible), play an instrument and spend time in nature.
L-theanine is generally safe for children though
A proper diet is crucial when it comes to development, get them engaged in any preferred type of exercise, limit screen time exposure & encourage regular proper rest. Vitamins might be a viable option as an adjunct treatment but do consult with someone who is qualified.
Nootropics like Noopept, Oxiracetam and Celastrus Paniculatus, in a stack with theanine, a gentle stim, EGCG, Theanine and Ashwaghanda can do wonders. It's important to experiment with your stack and, just as importantly, with your child's overall health condition and glucose tolerance prior to injecting nootropics into their diet. But the results are real.