Although many websites quote a Midrash saying Hashem told Avraham,
"I will give your descendants a special day for forgiveness: Hoshana Rabbah. If they are not forgiven on Rosh Hashana then let them try Yom Kippur; if not, then Hoshana Rabbah,"
not a single site I found quoted the actual source.
Although this answer addresses the same question, the insightful post doesn't directly source the Midrash.
Where is this precise Midrash?
Hagahot 216 to Minhagim (Tirna) on Sukkot quotes this statement. It's also brought in Matte Moshe 957, who seems to have copied directly from Minhagim. Neither explicitly says it's a midrash. However, Pa'neach Raza on Emor, who only makes reference to the first few words, does quote it as a midrash.
Here is the text from the Hagahot to Minhagim (I put what appears to be an interpolated explanation in parentheses):
למה נקרא שמו הושענא רבה אמר הקב"ה לאברהם אני יחיד ואתה יחיד אתן לבניך יום המיוחד לכפר בו עונותיהם וזהו הושענא רבה (פי' שמי אהיה בגימטריא כ"א ואתה בכ"א עשרה דורות מאדם ועד נח ועשרה דורות מנח עד אברהם והושענא רבה כ"א ימים לחודש תשרי) אמר לו הקב"ה לאברהם אם אין כפרה לבניך בר"ה יהיה בי"כ ואם לאו יהיה בהושענא רבה
Why is it called Hosha'na Rabba? God said to Abraham, "I am unique and you are unique. I will give your children a unique day to atone for their sins," and this is Hosha'na Rabba. (Explanation: My name אהיה has a numerical value of 21; you are in the 21st generation, ten generations from Adam to Noah and ten generations from Noah to Abraham; and Hosha'na Rabba is the 21st day of the month of Tishrey.) God said to Abraham, "If there is no atonement for your children on Rosh Hashshana, there will be on Yom Kippur; and if not, there will be on Hosha'na Rabba."
I haven't found this midrash attested by any earlier source of midrashim. It seems to have been known to the rabbis of Ashkenaz starting from around the 14th-15th century, and maybe it was also composed in Ashkenaz.
