Here the 1841 British edition replaced the archaic, biblically styled use of mine with the modern use of my. In Early Modern English, forms like mine were expected before vowel-initial nouns such as epistle. In this case, the subsequent LDS edition (1849) restored the original mine. As described under Omni 1:10, the 1841 edition frequently made this change from mine to my.
Overall the text has four instances of my epistle and seven of mine epistle (including this one here in Alma 60:36). The four instances with my occur first (from Alma 54:11 through Alma 55:2), followed by all seven of the instances with mine (from Alma 55:3 through Alma 61:21). The critical text will in each case of mine versus my follow the reading of the earliest textual sources, thus mine epistle here in Alma 60:36.
Summary: Maintain in Alma 60:36 the archaic use of mine before epistle, the reading of the earliest textual sources, including 𝓟 (𝓞 is not extant here).