"Who did write .../Who wrote ...?"

[Odessa Dawn]

Who did write this letter?
Who wrote this letter?

Would it be correct if I used the first one?

 

[GoesStation]

It's correct if it follows an incorrect statement about who wrote the letter.

A: I've got Jim's letter here.
B: Jim didn't write that.
A: Oh, I see. Who did write it (rather than the person I thought)?

"Did" is heavily stressed in this usage in spoken English.

 

[GoesStation]

Many people learning English discover they can express a past action with did + bare infinitive, and give up learning irregular simple past conjugations and other complicated bits of the past tense. Don't do this. The problem is that this usage carries a distinct meaning; it's an emphatic form.