In the text of the The Apostolic Tradition (3rd Century AD), we find the following teachings about when to pray.
If you are at home, pray at the third hour [i.e., 9:00 a.m.] and bless God. But, if you are elsewhere then, pray to God in your heart. For at that hour Christ was seen fixed to the wood. Hence even in the Old Testament the law ordered that the bread of proposition should be offered at the third hour as a type of the body and blood of Christ; and the immolation of the irrational lamb is a type of the perfect Lamb. For Christ is the shepherd, and he is also the bread that came down from heaven [see John 6:41].
Pray likewise at the sixth hour [i.e., noon]. For when Christ was fixed to the wood of the cross the day was broken and there was a great darkness [see Matthew 27:45]. So let a powerful prayer be offered at that hour in imitation of the voice of him who prayed and caused darkness to overshadow all creation because of the unbelieving Jews.
Let a great prayer and a great blessing be offered also at the ninth hour [i,e., 3:00 p.m] to imitate the manner in which the soul of the righteous praises God, who does not lie, who remembers his holy ones and has sent his Word to glorify them. At that hour Christ, pierced in his side, poured forth blood and water [see John 19:34] and, illuminating the rest of the day, brought it to evening. And so, when he began to fall asleep, while causing the following day to begin, he imaged the resurrection.
Pray as well before your body rests on its bed. But toward midnight, rise up, wash your hands and pray…It is necessary to pray at that hour. For the ancients who have recounted the tradition to us told us that at that hour the entire creation rests for a moment in order to praise the Lord: the stars, the trees, the waters stop for a short space of time, and the whole army of angels who serve him praises God at that hour along with the souls of the righteous. That is why those who believe should hasten to pray then. And the Savior bears witness to this when he says, “Behold, a cry is heard in the middle of the might of one saying, Behold, the bridegroom is coming; rise up to meet him” [Matthew 25:6]. And he continues, “Watch,therefore, for you do not know the hour when he is coming” [Matthew 25:13].
And at cockcrow rise up and pray once more. For at that hour, at cockcrow, the children of Israel denied Christ [see Matthew 26:74-75 par.], whom we know by faith. In the hope of eternal light at the resurrection of the dead,our eyes are turned toward that day.
(Boniface Ramsey, Beginning to Read the Fathers, 175-176)