When a father dies and leaves his 2nd wife everything in his estate does his birth children have any claim to part of the estate?

If you're in the US, he can leave his property to whomever he chooses as long as his will is properly drafted for his state. He is not required to include his children in the will but some states require they be specifically mentioned if the parent wants to disinherit them. Pretty much the only way to successfully contest this would be if you can prove that he was not mentally competent when he wrote the will. You need to discuss the situation with a local estate attorney.