AKs 3bet pot post flop play, turn call or fold?

Check fold OTF is totally standard here. With a cbet OOP you just often get yourself in trouble. I usually advice to be a bit conservative when cbetting out of position. That makes sure you have enough decent hands in your checking range so you will not be check folding too often. But the fact that you have to fold vs a stab doesn't mean you should cbet. If the hand is crap it is crap.

We could use Baluga theorem that says to fold less than 2 pair hands vs a turn raise. That is because those turn raises are often too value heavy. In today's games people start to bluff raise there more but let's remember that villain opened from UTG in full ring game and called a big 3bet. I very much doubt that he raises you with AQ or AJ. He could have 88,TT,ATs.

So the hands you listed: AQ, AJ, QhJh,KhQh,KhJh
I doubt those AQ and AJ raise. The rest would be ok as bluff raises but QJs,KJs would be already too weak for me to call a 3bet from UTG in 6max. If we don't have reads on villain it might be a bit loose to put those in his range, especially KhJh.

Problem here as well is that you betting to much on the turn to get away if he's shoving on you. Half pot bet is big enough on the turn I think.

Cheers,
SDK1987

I cbet bigger the turn, drawheavy, two possible flushdraw and J9s, 67s, KQs straight draw too, but you right enough half cbet the turn. Thank you!

Pre-flop standard.
The cbet on the flop is ok. But OOP I prefer to check here. The reason is: this board doesn't favor your 3bet pre-flop. You'll see a decent opponent floating here or even raising you very often. And then you'll be in a very tough spot.

Turn is a bet. In this case you're not bluffing, but even if it was the case, the ace is the best card to do it on.
You protect your hand against the flushdraws and get value off some hand with an ace, that's consistent with his call to your 3bet pre-flop.
I think I'm folding to the shove. He called your 3 bet, called your flop bet and shoves OTT after a 2nd barrel. I think this screams value.
A very good opponent would know this is a great spot to throw a bluff in and could shove to force your fold. But I don't think that's an NL5 level skill.

checkfold flop
as played bet/call due to huge number of draws - he could be reshoving for protection with worse so you cant fold.