Ex husbands children & payments?

I have recently got married & my wife has two children to her ex. They currently have a week on/week off arrangement with parenting rights. My wife was unemployed and now is pregnant to me. The ex has told me I have to pay for his & my wife's childrens education. This doesn't seem right to me. My wife can't pay the private school fees as she is unemployed. Do I have to pay them? (I am happy paying for their housing, food & general education at a state school).