Just wanted to share my personal experience with a similar issue from this past year, as I had been debating between submitting a paper that was unrelated to my field of interest (both in terms of geography and chronology), submitting the prospectus for my undergraduate thesis, or trying to write and submit a chapter of my thesis before deadlines. For what it's worth, I ultimately decided to submit the unrelated paper and, as @TMP recommends, spent considerable time and effort in my SOP to demonstrate familiarity with the historiography, etc. While this situation was not ideal and caused additional stress, I was accepted into a few of my top programs and my writing sample topic did lead to interesting conversations with POIs! So, based on my own experience (take it as you will), I would recommend sending a paper that really showcases your writing and ability to use primary sources. If this happens to be a paper related to your field, even better!