In a letter (#301) to August Derleth, ca. mid-October 1934 we possibly learn of the sale. This could also be "Hawk of the Hills" or "Blood of the Gods":

My latest sales have been a 23,000 word Oriental adventure yarn to Top- Notch, and a two-part Conan serial to Weird Tales; no sex in the latter.

To Alvin Earl Perry, ca. early 1935 (letter #306) Howard writes:

The first character I ever created was Francis Xavier Gordon, El Borak, the hero of “The Daughter of Erlik Khan” (Top-Notch), etc. I don’t remember his genesis. He came to life in my mind when I was about ten years old.

A letter (#313) to H.P. Lovecraft, ca. May 1935 gives us:

Lately I’ve been trying to break into some new markets, specializing on the adventure angle. Top Notch has bought four long stories from me, giving me the cover design on the last issue,4 and I’m trying to make it regularly.

Top-Notch bought only four Howard stories: “Swords of Shahrazar,” published October 1934; “The Daughter of Erlik Khan,” December 1934; “Hawk of the Hills,” given the cover illustration, June 1935; and “Blood of the Gods,” also with cover illustration, July 1935.