In Yeni Hitit, a Turkish method, two sentences :

Onunla öğrenciyken tanıştım.

and 

Öğrenciken çok çalışkan değildim.

Now my question is : 

The suffix /ken/ take (y) or not with a word who ends with vowel ?

Yes, it takes. 

Istanbuldayken, evdeyken, okuldayken....

(y)ken suffix can also follow after verbs, and mostly it is with verb which is in aorist, then Y doesn´t preceed.

giderken, gelirken, koşarken

also with nouns, adjectives for example  açıkken--->  while it is or while it was open.

Ben küçükken ---->  While I was small / while I was a small child.

It can be written separately as iken

i.e. öğrenci iken, öğretmen iken

But if we join it to a word, then if that word ends in a vowel we need to add a y so that it flows smoothly

öğrenciyken, öğretmenken

Thanks for the answers. It´s very kind of you.