Friday, September 22 is our Islamic New Year, and it’ll be the year 1439; the date marked by the arrival of Our Beloved Messenger ﷺ to Al-Madīnah, The City Illuminated with Love. The first month in the calendar is Muḥarram. It’s a great time to fast, specifically the 10th day [ʿĀshūrāʾ].
We should all try to fast on ʿĀshūrāʾ, The 10th of Muḥarram, which is Sunday, October 1. If possible, fast the day before or after as well.
Muḥarram — This is the 1st month of the Islamic Lunar Calendar. The Messenger of God ﷺ referred to it as “The Month of God [Shahr Allāh]”, and it has certain virtues. It’s also possibly a month of increased forgiveness .
The Messenger of God ﷺ said: “Aside from Ramaḍān, the best fasts are the fasts of The Month of God, Al-Muḥarram.” [2, 3, 4, 5]
ʿĀshūrāʾ — This is the 10th day of Muḥarram. Everyone should try and fast this day.
Reward: The Messenger of God ﷺ said: “Fast on ʿĀshūrāʾ. Doing so will forgive your sins of the previous year.” [6, 7]
Encouragement: Ibn Abbās (Rḍ) said: “I never saw The Prophet ﷺ wanting to fast a day more than ʿĀshūrāʾ…” [8, 9] In regards to ʿĀshūrāʾ, The Messenger of God ﷺ said: “Fast!” 
Reasoning: Ibn Abbās (Rḍ) mentioned that the Jews of Al-Madīnah used to fast on ʿĀshūrāʾ because The Exodus [The day Moses (ع) escaped with the Israelites] occurred on that day. The Messenger of God ﷺ responded saying: “We have more right over Moses, so fast [on this day].” [11, 12]. It’s also possible that The Messenger of God ﷺ added on saying: “So differ from the Jews, and fast the day before or after as well.” 
Fasting The 9th As Well: The Messenger of God ﷺ said: “If I’m still alive next year, I will definitely fast the 9th as well. [Meaning, in addition to the 10th]” [14, 15]. Since the 9th is on a Friday, you can get #doubleSunnah. And based on , it would be okay to fast the 11th as well. If you want to be OG, you can fast from the 9th, up until the 15th and be #superSunnahSquad.
- The other narrations mentioned here should be give preference in terms of reliability for proving the months’ virtues. ↑
- There is discussion about this ḥadīth, as to whether The Messenger of God ﷺ actually said “after it”. There are other narrations mentioned in  that The Prophet ﷺ just said the 9th and 10th. ↑
- Because The Messenger of God ﷺ would regularly fast on Fridays. [16, 17, 18] ↑
- There’s discussion as what days one can/should fast. To list them in brief: 10th, or 9th & 10th,, or 10th and 11th, or 9th & 10th & 11th. Due to the differing narrations, the days which are to be fasted are up for discussions. Some scholars opined that there is no virtue in adding the 11th. And others have said that no one should fast all three: 9th & 10th & 11th [referring to it as a innovation [bidʿah]]. It is also narrated that Ibn ʿUmar wouldn’t even fast ʿĀshūrāʾ, unless it coincided with his normal fasting routine.  ↑
- Because The Messenger of God ﷺ highly advised fasting the “White/Bright Days” which are the 13th, 14th, and 15th. [20, 21, 22, 23] ↑