Does training my vertical jump stunt my growth in any way?

I am interpreting this question as asking if concerted effort to increase his ability to jump high might stunt his growth. The answer is an emphatic, "No!" In fact, such exercise, if anything, will promote growth and development and enhance the uptake of calcium by the child's bones, thereby helping to prevent later osteoporosis.

No, exercise in general promotes a healthy lifestyle. No particular form of exercise will stunt growth. Eat a nutritious diet, get a lot of sleep, and then continue exercise in any form, for best growth. Good luck!