Praise be to Allah.
What appears to be the case from your question is that you are taking the cortisone by mouth, either in the form of pills or liquid medicine. If that is the case, and you took it after you were certain that dawn had broken, then that invalidated the fast, and you have to make up that day after the end of Ramadan, because you were sick, and Allah, may He be exalted, has granted a concession to the sick person allowing him not to fast during Ramadan, and to make up the days when he did not fast. Allah, may He be exalted, says (interpretation of the meaning):
“and whoever is ill or on a journey - then an equal number of other days”
But if the cortisone is taken in the form of an injection (via a needle), then it does not spoil the fast, because the most correct scholarly view is that injections do not spoil the fast unless they are for the purpose of nourishment, such as the solutions that are given to some patients. For further discussion concerning that, please see the answer to question no. 38023.
You mentioned in your question that you took the medicine after the mu’adhdhin gave the adhaan. In most cities and towns, the mu’adhdhins rely on timetables that give the times for prayer according to astronomical calculations, and they do not rely on sighting the dawn with their own eyes, because that is not usually possible in cities and towns.
There is a well-known difference of scholarly opinion concerning the errors in some of these timetables with regard to the time for Fajr prayer. In some Muslim countries, committees were formed and some of the committees whose members are trustworthy reached the conclusion that the break of the true dawn is later than the time mentioned in these timetables; the time difference is sufficient for one to take medicine, or even longer than that.
This is the view of some scholars, such as Shaykh al-Albaani and Shaykh Ibn ‘Uthaymeen (may Allah have mercy on them both), and is also the view of some specialists in astronomy.
The number of minutes varies according to the season, and according to the angle that the state used to work out the onset of dawn by astronomical means.
Because the scholarly view that there are such errors is so well known, these timetables cannot be relied upon to determine the time of dawn with certainty. Allah, may He be exalted, has permitted the fasting person to eat and drink until he is certain that dawn has come. Allah, may He be exalted, says (interpretation of the meaning):
“And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]”
What appears to be the case – and Allah knows best – is that you took the medicine shortly after the adhaan, when there was no certainty that dawn had come. Therefore your fast is valid. But if you took the medicine a long time [after the adhaan was given], you have to make up that day.
The best is for the Muslim to stop eating and drinking according to the timetable in all cases, because that is more prudent and more likely to not affect his fast.
See the answer to question no. 66202.
And Allah knows best.