While there is nothing wrong with giving supplements to a child, it is always a good idea to focus on food first and then use supplements in a targeted manner.
A good way to approach this is to focus on giving your child a superfood boost a day -- something that is packed with nutrients. Here are a few examples:
Bone broth -- this is usually a hit with kids who generally enjoy soupy noodles or congee. Make a robust broth by boiling bones (organic, hormone free, where possible) with some vegetables like celery, carrots, onions and garlic. You can use any flavoring you wish, and herbs work well in this as well. The key is to boil the bones for a good 4- hours, or overnight in a slow cooker. Broth can be stored in the fridge for 3 days and can be frozen for a month. Use this to make soup based dishes for your child.
Smoothies -- this can be made with yoghurt, a fresh coconut (water + cream) or a non-dairy alternative like oat milk as a base. To this, you can add a number of things - fruit, leafy greens, nut butters like almond or unsweetened peanut butter, avocado, and even some steamed and frozen cauliflower. Its a food idea to start slow using a base and fruit your kids enjoy. As they get used to it, you can layer on the other boosters to the smoothie.
Supplements do have a place but it is a good idea to know what your child may be deficient in. There are some tests that can help identify that. At TNC, we see a lot of kids who are deficient in Vitamin C, Zinc, B-vitamins and may have low levels of probiotics in the gut, especially if they have taken a lot of antibiotics.