Everyone who is in the USA other than foreign diplomats and their families is subject to the jurisdiction of the USA.<quoted text>Aliens have never been "subject to the jurisdiction, thereof", this is only a status held by citizens.
"All persons born or naturalized in the US and "subject to the jurisdiction, thereof" are citizens." Who are subject to the jurisdiction, thereof?
“A citizen of the United States is held by the courts to be a person who was born within the limits of the United States and subject to their laws.” Senator Jacob Howard, Cong. Globe 39th Cong., 1st Sess, 2765 (1866).
“Is not the child born in this country of German parents a citizen? I am afraid we have got very few citizens in some of the counties of good old Pennsylvania if the children born of German parents are not citizens.”-Senator Lyman Trumbull, Cong. Globe 39th, 1st Sess 498 (1866).
“Who are natural-born citizens but those born within the republic? Those born within the Republic, whether black or white, are citizens by birth—natural-born citizens.” John Bingham, Cong. Globe 37th Cong., 2nd Sess. 1639 (1862)
"It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore every child born in England of alien parents was a natural-born subject unless the child of an ambassador or other diplomatic agent of a foreign State or of an alien enemy in hostile occupation of the place where the child was born.
III. The same rule was in force in all the English Colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the Constitution as originally established." (US Supreme Court ruling in the Wong Kim Ark case.)