If your cousin's half-sister gives birth, and you are not related to her, the child is not directly related to you biologically. The child would be your cousin's half-sister's child. In this case, the child would be your cousin's half-niece or half-nephew. The "half" part indicates that you and your cousin share one biological parent, but your cousin's half-sister comes from the other parent. Therefore, there is a partial blood relation between you and the child, but not a direct one.