The name "Ancient of Days" appears only one place in the Bible, in the book of Daniel.
It refers to God the Father, seated on the throne in all His glory and power and receiving all the praise and worship due Him.

Daniel 7: Daniel's Vision of the Ancient of Days
In the first year of Belshazzar king of Babylon, Daniel had a dream and "visions of his head" while on his bed. Then he wrote down the dream, telling the main facts. Daniel spoke, saying, "I saw in my vision by night, and behold, the four winds of heaven were stirring up the Great Sea...

"I watched till thrones were put in place, and the Ancient of Days was seated; His garment was white as snow, and the hair of His head was like pure wool. His throne was a fiery flame, its wheels a burning fire; a fiery stream issued and came forth from before Him. A thousand thousands ministered to Him; ten thousand times ten thousand stood before Him. The court was seated, and the books were opened.

..."I was watching in the night visions, and behold, One like the Son of Man, coming with the clouds of heaven! He came to the Ancient of Days, and they brought Him near before Him. Then to Him was given dominion and glory and a kingdom, that all peoples, nations, and languages should serve Him. His dominion is an everlasting dominion, which shall not pass away, and His kingdom the one which shall not be destroyed."

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