Thank you for your question!
First of all, I must inform you that there are no products, vitamins or supplements that have been shown to be effective or beneficial for the immune system in adults and children.
Instead, look to non-pharmacological measures: make sure your child is eating plenty of fruits and vegetables, getting adequate sleep, and ensuring good stress management if possible, among other things. If one of the children or members of the household is ill, simply maintain basic hygiene measures: avoid hugging if possible, do not share towels, and wash them often.
Finally, if your child is prone to colds, I strongly suggest, for maintenance and prevention, sinus hygiene with a saline solution like Hydrasense or Sinus Rinse.
This is the best option to prevent the accumulation of secretions. There is no maximum during the day, but it should be done at least 30 minutes before bedtime.
PS: for solid vitamins (chewable tablets, gummies, etc.), the minimum age is 3 years.
I hope I've been helpful to you, I'm still available if there's anything you need
Tom Samaha, pharmacist