I have not finished yet.
It's possible to put it after the negative auxiliary, have not-has not, in order to add emphasis.
I have not yet finished.
It's also possible to use "yet" to mean "still" without using the present perfect.
I have yet to finish to finish the report. = I still haven't finished the report.
I had yet to finish the report. = I still had not finished the report.
It's also possible to use "yet" to show contrast in the same way we use "but". Using "yet" shows a stronger contrast. It provides emphasis to the contrast.
It's freezing cold out, yet you still go outside with that thin jacket. You're going to catch a cold.