In the Little House on the Prairie television show, Caroline’s stepfather Frederick Holbrook is distraught over the death of his wife, Caroline’s mother in the season six episode Author, Author. In the episode, Frederick is convinced to write his autobiography, detailing the life he had and shared with Caroline’s mother.
We do see the book published at the end of the episode, after some trickery by Albert to wrangle the Mercantile into helping publish and sell the autobiography. After this episode, the published autobiography is never mentioned again, but it is known that Frederick returns to his home in the Big Woods as a published author.
This is the only episode that Frederick Holbrook appears in (other than in the pilot episode where we see him but he is portrayed by a different actor and never spoke in that pilot). There is no mention of him writing any more books.
Note: This does not follow the real life parents of Caroline Ingalls, although the names are accurate. In real life, Caroline’s mother passes away ten years after the death of her stepfather. And there is no record of either writing an autobiography.