Recently there has been many places that say Yom Kippur Katan prayers at Mincha on Erev Rosh Chodesh. What is the source and who composed the Yom Kippur Katan prayers?
who composed the Yom Kippur Katan prayers?
Little Yom Kippur in Judaism is a name for fasting and Taanit customs, and the saying of forgiveness, which is practiced every New Year's Eve, and when Rosh Hashanah begins on Saturday or Sunday, precedes "Yom Kippur" on Thursday. The custom of the custom is probably in Safed, and it is mentioned in the book "Menot HaLevi" by Rabbi Shlomo Elkabetz and in the Kabbalah by Rabbi Moshe Cordoviro. However, the custom was already well-known in Ashkenaz in the mid-15th century and is mentioned in the book "Collect justice".
What is the source?
This custom expresses an idea whose roots are already in the Bible (in the Book of Numbers, chapter 18, verse 15, when God commands the people of Israel to bring a sin offering on Rosh Chodesh), according to which Rosh Chodesh is a day of judgment and atonement for wrongdoing alongside being a feast day.
Later, this idea came to light (though vague) in the Talmud (Babylonian Talmud, Maskat Shavuot, page 9, page 2, and in the Babylonian Talmud, Maskin Chulin, page 5, page 2) regarding being the first-year sacrifice of God's atonement Supposedly for diminishing the light of the brick in the seven days of creation.
This is how the idea developed that because Rosh Chodesh is a Judgment Day, it is necessary to treat this day accordingly: seriously and imitating the practices of the Central Day of Atonement in the year, it is not Yom Kippur.
You can see the whole answer here including what nakE wrote that there are allusions to yom kippur katan in the pasuk and gemora and that yom kippur katan has been done at least since the 15th century.
This source answers why is the day of yom kippur katan on erev rosh chodesh and not on rosh chodesh itself and that is that since rosh chodesh is a happy day, they set the day for tefilah and fasting (for those who fast) erev rosh chodesh.