If you are going to deliberately misinterpret the meaning of the word "Jurisdiction" to apply it to illegal aliens, then I am going to deliberately misinterpret the word "Combatant" to apply it to illegal aliens.
I have argued this topic for seven years, and I have a mountain of statements from people in the past to throw at you, but I am not in the mood to look up all that crap.
I'll toss you this one though.
From the primary author of the 14th amendment, John Bingham.
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. There is no such word as white in your constitution. Citizenship, therefore does not depend upon complexion any more than it depends upon the rights of election or of office. All from other lands, who by the terms of your laws and compliance with their provisions become naturalized, and are adopted citizens of the United States; all other persons born within the Republic, of parents owing allegiance to no other sovereignty, are natural born citizens.