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:
You are advised to breastfeed your child, especially at this young age. If you choose to breastfeed, you may skip the fast and make up for it later.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Breastfeeding is required for the proper development of your child, as Allah has placed in breast milk immunity for the child. Therefore, you are advised to breastfeed your child, especially at this young age; baby formula cannot be a substitute for your milk.
If you choose to breastfeed, you may make use of the allowance to skip the fast, but you should make up for it later. If you think you cannot make up the fast soon, then you may do well to offer fidyah, which entails feeding a poor person per day of the month of Ramadan. You should also make up for any missed fasts whenever you can.
Now, coming to the fatwa you have read saying that it is enough for a breastfeeding mother to give fidyah in lieu of fasting, that was a view held by Ibn Abbas and Ibn Umar; however, it is not the opinion of the majority.
According to the majority view, fidyah alone would not suffice; rather, a woman in this situation needs to make up her fast whenever she is able. They have concluded this by making an analogy to those who skip fasting because of illness or travel, as Allah said: “(They) [shall fast instead for the same] number of other days (later on)” (Qur’an 2:185).
Having said this, I should also add that you may follow the opinion of Ibn Abbas and Ibn Umar if you find it hard to make up your fasts because of your exceptional circumstances.
Almighty Allah knows best.