It is appropriate that a supplicant should pay special attention about the timings of his prayer. Following are some of the most suitable timings for supplications:
A. Friday Day and Night
It has been narrated from Imam al-Baqir [a]:
"Every Thursday night till the end of Friday, Allah calls his believing servants from the Upper Heavens, inviting them towards Himself and announces: 'Is there any believing servant who before the day breaks asks forgiveness for his sins and I forgive him, is there any one who seeks anything from me and I grant his requirements, is there a believing servant, who cries for Me, and I respond?"'
Also, it has been narrated:
"Allah delays the grant of a supplicant's prayer and fulfilment of his needs until Friday."
Also, it has been narrated from the Holy Prophet [s]:
"The day of Friday is the most superior and exalted among all the days in the sight of Allah, even superior than the days of Eid-ul-Fitr and Eid-ul-Adha. He continued and said: 'there is a special particular hour on Friday, that at that time there is no one who desires anything permissible and proper, but Allah grants his requirements."
The Holy Prophet [s] continued: "During Friday there are two hours which possess special merits; firstly, the hour when the Imam of the Friday congregational-prayer finishes his sermon until the lines of congregational-prayer get readied for the prayer, and the other hour is the end of the day."
B. The noon (dhor) and afternoon (asr) of Wednesday, especially, for prayer and cursing of infidels.
C. During night (isha) a), it has been narrated that such opportunity and preference were not given to the past nations.
D. The first hour of the first half of the Night, it has been narrated from Imam al-Sadiq [a]:
"There is a particular hour during, the night, in which if a believer would offer the prayer, it is impossible but it would be accepted (by Allah). He was asked: 'which hour is it?' The first hour of the first half of the night', replied the Imam
Also, it has been narrated from the Commander of the Faithful Imam 'Ali [a]:
"It was at this hour that Prophet David [a] went out to fight against Goliath." Also he said: "Whoever prays during this hour, his prayer is granted but ...."
E. End portion of night till the dawn or the last one third of the night.
It has been narrated from the Holy Prophet [s]:
"Whenever the end portion of night arrives Allah looking at his servants says: 'Is there any supplicant so that I could grant his prayer? Is there any needy so that may I fulfil his needs? Is there any repentant so that I there could accept his repentance? Is there anyone offering apology so that I could accept it?"
In another tradition it has been narrated that Allah (the Glorious, the Exalted) says:
"O' righteous ones strive and o' sinners and transgressors stop doing it."
Also it has been narrated:
"Whoever sleeps in that portion of the night till the dawn, Satan urinates in his ears."
 Imam al-Baqir [a]: (57/675-114/372), the son of the fourth imam, he was present at Karbala at a young age. Because of changing political and religious conditions, among them the general revulsion following the events at Karbala, many people came to Madina to learn the religious and spiritual sciences from him. He trained numerous well known men of religion, and mainly for this reason is the first Imam 'Ali [a] from whom large numbers of traditions are recorded. He is buried in the Baqi Cemetery in Madina [Tr].