Are there references of Quran which talk about who can be exempted from fasting in Ramadan?
Yes, there is a very clear verse. Allah subhanahu wa ta'alla says,
فَمَن شَهِدَ مِنكُمُ الشَّهْرَ فَلْيَصُمْهُ وَمَن كَانَ مَرِيضًا أَوْ عَلَىٰ سَفَرٍ فَعِدَّةٌ مِّنْ أَيَّامٍ أُخَرَ يُرِيدُ اللَّهُ بِكُمُ الْيُسْرَ وَلَا يُرِيدُ بِكُمُ الْعُسْرَ وَلِتُكْمِلُوا الْعِدَّةَ وَلِتُكَبِّرُوا اللَّهَ عَلَىٰ مَا هَدَاكُمْ وَلَعَلَّكُمْ تَشْكُرُونَ ﴿البقرة: ١٨٥
So whoever sights [the new moon of] the month, let him fast it; and whoever is ill or on a journey - then an equal number of other days. Allah intends for you ease and does not intend for you hardship and [wants] for you to complete the period and to glorify Allah for that [to] which He has guided you; and perhaps you will be grateful. (Al-Baqarah:185)
Ibn Katheer says that this verse specifies who is temporarily exempted from fasting. The two categories include sick people who are unable to fast or fear that fasting will harm them, and travelers; however, the missed days need to be made up.
Ibn Qudamah explains in Al-Mughni that it is permissible for the following to not fast in Ramadan: menstruating women, postpartum bleeding women, travelers, young kids, insane people, disbelievers, and the sick. All of these need to make up their fast except for young kids when they reach ten years old, and disbelievers when they convert to Islam. As for the sick whose recovery is not expected, they need to pay for the days they did not fast.