First of all, all Muslims should bear in mind that Allah has permitted the fasting person to eat and drink until dawn comes. He, Most High, says: “… and eat and drink until the white thread becometh distinct to you from the black thread of the dawn …” (Al-Baqarah: 187)
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: “The exact cut off time for imsak (abstaining from food, drink, etc.) is the time of fajr; so if you ate until that time you did not incur any sin. Most of the time people confuse between the preferred time and the permissible one; the preferred time for imsak, according to scholars, is to finish sahur ten minutes before fajr. This ruling is based on a report from a Companion of the Prophet (peace and blessings be upon him): When asked what was the gap between the time they finished eating sahur with the Prophet (peace and blessings be upon him) and they prayed fajr, he said: “The gap between the two was sufficient enough for a person to read fifty verses of the Qur’an.” It is, however, wrong to conclude from this that we are not allowed to eat until arrival of fajr since Allah clearly states in the Qur’an, “Eat and drink until the white thread of dawn is distinct from the black thread (i.e., until the arrival of true dawn).”
Moreover, if one started eating sahur before fajr but while finishing your meal you crossed one or two minutes, then you need not worry about it so long as you do not deliberately make it a habit. Your fasting is still valid. You need not make up for those fasts.
Also, we need not worry if we ate a few minutes into fajr due to ignorance. As Imam Ibn Taymiyyah has ruled, it is within the spirit of the Shari`ah to assume that Allah does not take us to task for such mistakes. So don’t worry about what happened in the past; you don’t need to make up for those fasts.
Having said this, however, I must rush to state: In future you should try to be careful not to cross the limits, for Allah wants us to render our acts of worship as efficiently and diligently as possible.”