When a father remarries and dies and does not leave a will can his biological children from his first marriage obtain any of his estates?

Probably true, but it depends on where in the world the father resided.

It depends on the intestacy laws where you are located. In Virginia for instance, the surviving spouse of an intestate decedent would inherit 1/3 of property that would have been heritable through a will, while surviving biological children of the deceased, but not the spouse would inherit the remainder of the estate. So much depends on the location, and if you'll provide the one in question, you'll get way better answers.