Volume 3, Page 134: Fasting, applying kohl or eyedrops or anything else to the eyes
These acts are all permissible, even if some taste from it finds its way to the throat, as the eyes are not a passageway to the stomach. Anas reported that he would apply kohl while he was fasting.
This is the opinion of the Shaf'iyyah. Ibn al-Munzhir records the same opinion from 'Ata, al-Hassan, an-Nakha'i, al-Au~a'i, Abu Hanifah, Abu Thaur, and Dawud. It is related from the following companions: Ibn 'Umar, Anas, and Ibn Abu 'Aufa.
According to atTirmizhi, nothing authentic has been related from the Prophet concerning this question.
According to Jumhur(majority of) ulama, hijama does not break the fast. This opinion held by Imam Abu Hanifa, Imam Malik, Imam As-Shafi'i, also Ibnu Mas’ud, Ibnu ‘Umar, Ibnu ‘Abbas, Anas bin Malik, Abu Sa’id Al Khudri, and some of Salafus Shalih.
However, I found a note from ulama: Hijama during fast is makruh if this could cause a person to become weak/limp, and could even be haram if hijama really can make a person break the fast.