How close is the English word "father" compared to the original word used by Jesus in the Lord's Prayer? Jesus is said to have used the Aramaic word ABBA in the Lord's Prayer. The word was perhaps used by children to address their father and was similar to what toady's children address their father as Daddy. In a few languages besides English, I have seen that the word used is the one which has more formal and literary usage than the word Daddy which in many ways expresses the bond between the children and their earthly father. 

I would like to know what exactly the word used to address the Heavenly Father in the Lord's Prayer in ancient English was. Are there any authentic studies available from the side of Catholic Church on the passage, from ancient times to the modern,  of the Lord's Prayer with specific reference to the way of addressing it uses ?
Although Jesus was likely to have spoken Aramaic or Hebrew, the Gospels were preserved in Greek using the word πατήρ/πάτερ, as was noted in the comments; this became the Latin pater. In England up to the Reformation, liturgically the Lord's Prayer was always in Latin.

However, Wikisource has Old English (10th&ndash;11th century) and Middle English (14th century) versions&dagger;:


  Fæder ūre, þū þe eart on heofonum;
  Sīe þīn nama gehālgod,





  Oure fadir that art in heuenes,
  halewid be thi name;


The word was cognate with the modern English Father. Whether Fæder or fadir were as formal as "Father" is today is not easily discovered, but it's likely that they were not; children routinely addressed their parents as "Mother" and "Father" until comparatively recently, and OED does not have Dad/Daddy recorded until the 16th century.

&dagger; The later version is from Tyndale's Bible. The earlier source is not identified.