Fasting;Salaah

Assalaamu Alaikum Mufti. I have three questions and I’d appreciate it if you could answer them.
I owe 3-days of fasting for Ramadaan due to illness. I fasted 2-days but I discovered that I’ve eaten a few minutes after Fajr has started. I have fasted two days completely except for the 10 minutes after start of Fajr. Should I still fast these days or does it count.