The two are interchangeable in British English, although some people feel that the use of 'as yet' is rather verbose (uses more words than necessary). There is AS YET no prospect of the return of peace. Correct There is yet no prospect of the return of peace. This doesn't work with the 'yet' in this position There is no prospect of the return of peace yet. Correct There is not yet a prospect of the return of peace. Correct, but rather clumsy - I recommend using sentence 1, 2, or 3. There is not as yet a prospect of the return of peace. Correct He booked for today, but he hasn't checked in as yet. Correct He booked for today, but he hasn't checked in yet. Correct

As (of) yet is used for talking about something that has not happened or been done up to now. The of in the phrase is optional but it is what I use. yet = it might change in the future. as (of) yet = not talking about changing in the future. There is, AS OF YET, no prospect of the return of peace.(o) this is correct. There is yet no prospect of the return of peace. (x) I agree that this is not correct due to the structure. There is no prospect of the return of peace yet.(o) this means that you expect it to change in the future when using yet. There is not yet a prospect of the return of peace. (o) this is ok. 'not yet' is the phrase that makes it possible. There is not, as of yet, a prospect of the return of peace. (o) This is fine. He booked for today, but he hasn't checked in as OF yet.(o) Ok! He booked for today, but he hasn't checked in yet. (o) Ok! I added 'of' because it sounds more natural for me as an American English speaker. Now adding the context to your sentences will be what to check if you can use 'as (of) yet' or 'yet' to really know if the sentence communicates what you want to say. Let me know if that helps! Enjoy your studies.