Al-Bukhaari (1921) narrated from Anas that Zayd ibn Thaabit said: “We ate suhoor with the Prophet (peace and blessings of Allaah be upon him), then he stood up to pray.” I [Anas] said: “How long was there between the adhaan and suhoor?” He said: “As long as it takes to recite fifty verses.”
The Standing Committee (10/284) was asked: I read in some tafseers that the fasting person should stop eating and drinking 20 minutes before the adhaan of Fajr, and this is described as being on the safe side. How much time should there be between stopping eating and drinking and the adhaan of Fajr in Ramadaan? What is the ruling on one who hears the muezzin saying “al-salaatu khayrun min al-nawm (prayer is better than sleep)” and he says can still drink so long as the adhaan is still going on. Is this correct?
The basic principle regarding when the fasting person should stop eating and drinking and should break the fast is the verse in which Allaah says (interpretation of the meaning):“and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night), then complete your Sawm (fast) till the nightfall”
You stop eating before true dawn. ie. you stop eating before the fajr time has started.
So fajr begins at 3:10am for you, so you stop eating before that time.
Try to be cautious however, maybe stop eating 5-10 minutes (if possible) before this time Inshallah.
Use the time after to brush your teeth, do wudu, and start praying Fajr on time.
Also, if you or a male relative can talk to the Imam, please do so about this because you may not be the same Madhab as the given quote above.