Fasting is required in Ramaḍān but there are other fasts outside of that month which are recommended as well.
The month following Ramaḍān is known as Shawwāl and it is highly recommended to fast any six days of that month. The Prophet said, “Whoever fasted Ramaḍān and then followed it up with six days of Shawwāl, it is as if he fasted continuously.” That is because the Prophet taught that good deeds are rewarded at least ten times, so fasting Ramaḍān is like fasting ten months. By fasting six more days, it is like fasting sixty more days, making a total of 12 months, so it is as if you fasted the entire year.
The fasts of Shawwāl do not have to be done in order and may be performed on any day of the month. A common question I get is whether you can combine the intention of making up a missed fast and also have it count as one of the six fasts in Shawwāl. This should not be done because the Prophet said “whoever fasted Ramaḍān”, so if you missed fasts from Ramaḍān, you have not completed the month of fasting yet, so the purpose of earning the reward for fasting the entire year cannot be multiplied until that is completed separately. Some people find it difficult to make up missed fasts and complete the six in Shawwāl, so in that case they can finish the six first since those have a shorter timespan to complete.
If you would like to fast more regularly throughout the year then it is recommended to fast three days, preferably the 13th, 14th, and 15th of any given month [of the lunar calendar]. These are known as the ‘white days’ because the moon is at its largest size. It is also recommended to fast every Monday or Thursday, or both, because that was the habit of the Prophet.
It is also highly recommended to fast on the tenth of Muḥarram [known as the day of ʿĀshūrā’] and on the first nine days of Dhul Ḥijjah, with the ninth being more emphasized than the other eight days.
You may fast on almost any day as an act of worship. However, do not fast on the day of Eid al-Fiṭr, Eid al-Aḍḥā, and on the 11th, 12th, and 13th of Dhul Ḥijjah. Also, do not fast every day with the intention to continue throughout your life because that would weaken your body and make you accustomed to fasting, so it would lose its purpose. Lastly, do not try to fast for two days straight without breaking the fast in between. These were all practices prohibited by the Messenger of Allah.
[Shaykh] Mustafa Umar
 Muslim #1164