At fourteen my son said that he now has the right to refuse to spend the week-end with his father during his visitation week-end. Is this correct? We live in Georgia.

My son turned 14 years and says now he does not have to visit his dad when it is his visitation week-end. We live in Georgia. Is this correct?

No, he can decide at 18, before that if you do not take or supply your son to his father, the father can take you ( YOU not the son) back to court for contempt.

You can file a motion to change the court orders for visits and allow your son to testify

Have no idea where the 14 age comes in, unless you had that written into the court order.
But no, the court orders are valid and have to be followed until the child is 18