There is no "their citizenship" as you call it, and they are not "citizen children". They are illegal aliens, just like their parents. And their parents simmigratin status of illegal can and is determined within hours of their capture, illegally crossing the Mexican border. It is also the status of criminal of having committed a crime, ranging from misdemeanor to felony, depending on the number of offenses.
How is a child born in the US an Illegal alien. An alien mean he came from some other country...How the hell is a child born on US soil be from some where else? That is laughable.
They aren't. If their parents are illegal aliens they just entitled to our citizenship by birth. They are citizens of their parent's country. Many countries require that at least one parent be a citizen of their country in order for their newborn to qualify. There are legal aliens and illegal aliens. Learn to know the difference.