Third and 12 from the A 3 yard line. QB A12 under pressure scrambles in the endzone. In a desperate attempt to save a safety, he throws from the endzone to A68, who catches it one yard in the endzone and runs to the 7 yard line. What do you have? NFHS.

In my not so expert opinion,

Illegal touching. Since the foul occured in the end zone, you have a safety.

SouthGARef is correct. If an ineligible player who is behind the neutral zone, catches, bats or muffs a pass before it touches an opponent, it is illegal touching, a five yard penalty from the spot of the foul and loss of down. If he touches the pass beyond the neutral zone, it is offensive pass interference, a 15-yard penalty from the previous spot and loss of down.

Here the spot of the foul was in the end zone, so as SouthGARef says it is a safety.

Basic spot is the endzone. Safety.

So if the touch or catch by A68 occurred at the 1 yard line, we would have 4th and about 14.5 from the half yard line correct?

Yup.

Also, the basic spot would NOT be in the end zone. It's a loose ball foul, so the "basic spot" would be the LOS. The enforcement spot is in the endzone however because of the all-but-one enforcement. But now we're just splitting hairs...

Yep,

If he'd only committed what is normally the worse of the two fouls, he would have saved his team 2 points.