Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If you have deliberately taken the medicine after the Fajr adhan, then you have invalidated the fast, and you should make up for any missed days after Ramadan.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Allah says: “Eat and drink until the white thread of dawn becomes distinct to you from the black thread of night.” (Al-Baqarah 2:187)
Accordingly, we must refrain from all consumption or intake of food or drink from the beginning of Fajr (dawn) until sundown. This, according to scholarly consensus, is a necessary condition for the validity of the fast.
Therefore, if you have deliberately taken the medicine after the Fajr adhan, then you have invalidated the fast, and you should make up for any missed days after Ramadan.
If, however, you did so unknowingly, then your fast is still considered valid. The Prophet (peace be upon him) said, “Allah has forgiven my Ummah for their sins borne of ignorance and forgetfulness as well as due to coercion” (Ibn Hibban).
Having said this, I should remind you that, if you are sick, you need not worry about your action, for you are exempt from fasting, especially if you are suffering from a condition that requires taking medication during the day.
You only need to make up for the fasts you have missed at a later time when you fully recover. If, however, you do not expect to recover, then you only need to give fidyah (expiatory compensation).
Fidyah consists of feeding a poor person for each day of fasting you have missed. In Canada, the monetary value of fidyah has been estimated to be equivalent to a minimum of ten Canadian dollars at the time of this writing in 2014.
Almighty Allah knows best.