"…didn't finish…yet" versus "…haven't finished…yet"

• If you worked on it yesterday, stopped yesterday before finishing then, and don't want to say anything else about whether you will or can continue or not, but more likely that you are done for good (like a one-time test), then:

  I didn't finish it.

• If you worked on it yesterday, stopped yesterday before finishing, and want to imply that you are still planning on working on it, then:

  I haven't finished it.

  or with a bit more emphasis on the expectation of continuing

  I haven't finished it yet.

• The sentence

  *I didn't finish it yet.

sounds off, because "didn't" isn't particularly continuous, but "yet' implies an expectation or possibility, and so also a continuing act.

The sentence "I did not finish it yet" is incorrect because of mismatched tense. The phrase did not finish is in the past tense, while the word yet indicates that the task is ongoing (present tense), which creates a contradiction.

The sentence "I have not finished it yet" is correct because the phrase have not finished is in the present tense and can be safely used with "yet". In fact, the word "yet" is not strictly necessary. "I have not finished" would carry the same meaning.

“I haven't finished it yet” is definitely a much more natural-sounding version but “I didn't finish it yet” might also be acceptable (though a bit more awkward).