Coughing is a common but potentially concerning symptom. I would encourage you to have your child evaluated by his pediatrician.
A cough is a normal reflex. We have developed a the reflex to clear the airways of dirt, inflammation or other obstructing materials. That is to say, if your child is coughing that suggests there is something in the airway that needs to be cleared. That can either be something small (like normal airway mucus) or something more serious (like and infection).
As for what could be causing this, there could be a few things to rule out. One would be an infection. Another possibility is a spasm of the airway. This can be caused by asthma
or other allergies. It is important to rule this out in young children. Another possibility that should be ruled out is that there is a problem with swallowing. There are a few problems that should be ruled out: A Tracheo-esophageal fistula is a problem where the air pipe (trachea) somehow connects to the food pipe (esophagus). Therefore with feeding the airway gets clogged and requires a cough.
These fits should be investigated. While hopefully a normal cough, this must be investigated. Good luck!