when you quit a level prior to completing it you gain some AP but not as much as if you had completed it (I think its around 0.25 * currentPercentComplet * completionAP

but this lowers the reward amount if you select the map again.

Is this intended ? if so what benefit could be gained from quitting early since you're locking yourself out of the lost AP

it is intended

the only reason you would ever abort a level is to be able to start another level, either because the current level is bugged, or to try out a new feature which is not on the current map

Quitting a level rewards you with 0.667 * currentPercentComplete * completionAP.
Restarting a quitted level rewards you according to the formula above, minus the AP you already collected.
Quitting is not worth it long term. Short term, it might reward enough AP to purchase an advancement. Alternatively, you can scout out a level, quit and restart with some knowledge, but usually the time to complete from zero is greater than the remaining time to finish a botched level.

So quitting doesn't actually cause you to miss out on any AP it just doesn't let ypu quit and get AP over and over. ok that makes way more sense. thank you.

it does cause you to miss out on AP

if you quite a level halfway, you get a portion of the AP, but you will not get the AP next time you play the level.
so on your next run for the level, you will have played the level 1,5 times, but only gotten 1 times the AP.

Let's explain better:
Let's say the level is valued at 100 AP upon completion. You play 30% of the level and quit. You receive 0.667 * 0.3 * 100 = 20 AP. The level will still be valued at 100 AP, with 20 AP already redeemed.
You restart the level. If you quit again before conquering 30%, you receive no AP. If you conquer more, you will get partial AP. At 45%, you get 0.667 * 0.45 * 100 = 30 AP, 20 of which were already redeemed, so you get an extra 10, and the value of the level will be 100AP, with 30 AP already redeemed.
Now if you complete the level on the third run, you will get the remaining 70 AP. The value of the level once completed will decrease for a replay to about 66AP.

^ replay decreases to about 70AP, 70% of the original.

Overall you don't miss out on AP, you only lose the time invested in playing a level that you aborted. You still have to finish the level to unlock the next one (unles you use the Skip Level power).