Q: Is it permissible to fast on the days of Tashriq especially if it is a day that I normally fast such as a Monday, Thursday, or the "white days" etc.?
A: Fasting, be it voluntary or obligatory e.g. a make-up day of Ramadan, on the days of tashriq (11, 12, and 13 of Dhul-Hijjah) is not valid based on the hadith which states, "The days of Mina are days of eating and drinking" (Muslim).
The only exception to this rule is the fast done by a pilgrim of either mutamatti or qarin status who does not have a sacrificial animal. This is based on the statement of Ibn Umar and Aisha who said, "The days of tashriq were not permitted for fasting except for the one who has no Hady i.e. a sacrificial animal for hajj" (al-Bukhari).
Source: Sharh al-Muntaha & Kashshaf al-Qina