Is a husband obligated to provide for his wife and her child, and is it permissible to annul the marriage contract and disavow the child's lineage, if a man marries a previously married woman who is three months pregnant, and the child is registered in his name six months later due to financial coercion?

Since the pregnancy preceded the marriage, you have no relation to the child and are not obligated to spend on him, and you must disavow him. As for his mother, you are obligated to spend on her because she is your wife, in consideration of those who deem valid the marriage to a pregnant woman due to fornication. You may divorce her if you do not desire her, although it is better to keep her if it is possible for life to continue and for her to be reformed.