For Medicaid to pay for a child's diapers the child must be at least 4 years old or older and have a medical condition such as incontinence or the inability to get to the bathroom or not be able to be toilet trained.
Sometimes Medicaid or other health insurance will help cover the cost of the child's diapers at age 3 if they have a medical diagnoses that requires them to wear diapers.
Before age 3 or 4 years old parents are usually expected to pay out of pocket for their child's diapers because they are needed normally after a child is born.
If you've tried to potty train the child by 3 or they cannot be potty trained due to a mental disability or they have incontinence then Medicaid or other health insurance will pay for the diapers.