Legal Question in Family Law in Illinois

He can try anything. The real question is can he succeed. If the facts as you state them are true, he doesn't really stand much of a chance at succeeding. Depending on what kind of a man he is, he may just be angry about the breakup and be striking out with no real intention of trying to get custody of the child. OTOH, he may be serious, either way you should get your ducks in a row by consulting with an attorney in your area and deal with the question of establishing paternity and child support. If he wants visitation, it is up to him to ask the court to set it up. You should not lose any sleep over his idol threats but you should be prepared. Good luck to you.