An author of science fiction repeatedly finds that no sooner has he published a new work than he finds that that it appears as though he had plagiarized it because it is suddenly listed as an already published work. The author suspects a time-traveler, from the future, copies his stories then travels to a pre-publication date, presents them as his own, and has them published, thus, “beating the true author to the punch!”
"Who's Cribbing", an epistolary short story by Jack Lewis, also the answer to this old question; first published in Startling Stories, January 1953, available at the Internet Archive. The text is also available at Becca's Book Blog. You may have read it in one of these anthologies.
In the story, the science fiction stories written by Mr. Jack Lewis (the protagonist has the same name as the real author of "Who's Cribbing?") are not published, they are rejected as unoriginal by the editors to whom they are submitted, as in this letter from Doyle P. Gates, Science Fiction Editor of Deep Space Magazine:
We are returning your manuscript, "The Ninth Dimension." At first glance, I had figured it a story well worthy of publication. Why wouldn't I? So did the editors of Cosmic Tales back in 1934 when the story was first published.
As you no doubt know, it was the great Todd Thromberry who wrote the story you tried to pass off on us as an original. Let me give you a word of caution concerning the penalties resulting from plagiarism.
Mr. Lewis puts forward his time-travel theory in this letter to Mr. Gates:
It seems all my stories are being returned to me by reason of the fact that except for the byline, they are exact duplicates of the works of this Todd Thromberry person.
[. . . .]
Yet in the interest of all mankind, how can I get the idea across to you that every word I have submitted was actually written by me! I have never copied any material from Todd Thromberry, nor have I ever seen any of his writings. In fact, as I told you in one of my letters, up until a short while ago I was totally unaware of his very existence.
An idea has occurred to me however. It's a truly weird theory, and one that I probably wouldn't even suggest to anyone but a science-fiction editor. But suppose—just suppose—that this Thromberry person, what with his experiments in electronics and everything, had in some way managed to crack through this time-space barrier mentioned so often in your magazine. And suppose—egotistical as it sounds—he had singled out my work as being the type of material he had always wanted to write.
Do you begin to follow me? Or is the idea of a person from a different time cycle looking over my shoulder while I write too fantastic for you to accept?