Can you leave and return for Visa ?

Hello everyone! I have a bit of a dilemma here. So I am currently in turkey on language course visa until June 16, 2023. Will I be able to fly to Greece or Georgia to complete an E visa on June 10th that would be valid for 90 days, so I am able to stay in the country until September 14?
I am an American citizen.

OR , I was thinking of just leaving May 18 before my visa expires because I already have a ticket booked August 16 2023 to return back to Türkiye from USA with a valid E-visa.
-@irismylife4you

The problem with turkey is that you can no longer do visa runs. Meaning that you leave the country, and come back and they give you another 90 days. The European union forced them to adopt the same standards that all EU countries are adopting now.

Which is that you can only stay 90 days out of 180 days.

If you had an ikhemet and it is expiring and have stayed in turkey for 6 months to a year then you can leave, and get a new visa, and then come back because the 90 out of 180 days no longer apply to you.

@irismylife4you try to renew your residence permit before traveling, it's the best way to stay in Türkiye.

Hello I'm a student studying in turkey, my ikamet expired 11 days ago outside of turkey, can i now reenter using my passport, i hold a Jordanian passport, does the 90 out of 180 days apply to me in this case or it doesn't because i was staying on ikamet