وَإِذَا سَأَلَكَ عِبَادِي عَنِّي فَإِنِّي قَرِيبٌ أُجِيبُ دَعْوَةَ الدَّاعِ إِذَا دَعَانِ فَلْيَسْتَجِيبُوا لِي وَلْيُؤْمِنُوا بِي لَعَلَّهُمْ يَرْشُدُونَ
And when My slaves ask you (O Muhammad sallallāhu alaihi wa salam) concerning Me, then (answer them), I am indeed near (to them by My Knowledge). I respond to the invocations of the supplicant when he calls on Me (without any mediator or intercessor). So let them obey Me and believe in Me, so that they may be led aright. (Al-Baqarah: 186)
Supplicating to Allāh whilst fasting is one of the times where supplications are most likely to be answered. This is because Allāh mentioned this verse within the verses of fasting. Especially since He spoke about it at the end of His speech regarding the verses of fasting.
Some of the scholars said, There is another benefit extracted from this verse: it is befitting to supplicate at the end of the fasting day, (i.e. before Maghrib, at point of opening fast).
This is one of the best times to supplicate, as the fasting person is weak and the weaker a person is, the more softer and open his heart is. This person is more likely to turn repentantly to Allāh and to lower and submit himself to Allāh.
1. Shaykh Uthaymīn’s Tafsīr Al-Baqarah Vol.2 Pg 344
2. Majmū’ Al-Uthaymīn Vol. 19 Pgs. 323-324