This seems to be related https://www.duolingo.com/comment/26607029 but they discuss different forms. Your word order looks really strange. Maybe possible in colloquial English but I don't think it is possible at all in any standard English. Or it is very marginal, compare the frequency https://books.google.com/ngrams/graph?content=I+yet+have+not%2C+I+have+not+yet I have not yet is 5000x more common than I yet have not.
As a native (US) English speaker, I don't think anyone would use "yet have not written" in speech or in writing. "Have not yet written," on the other hand, would be used quite often, although that construction splits the verb. That used to be a bad thing grammatically, but it may be becoming more acceptable in these days of loosened standards...
“Ještě” can be translated as “yet” or “still”. However, yet and still are not always interchangeable. In this word order the use of “still” would be perfectly acceptable English — “I still have not written the letter.”