Answer: Jesus, several times in the Bible, is referenced as sitting at the Father's right hand in heaven or being exalted by it.
The Lord said unto my Lord, "Sit at My right hand until I make Your enemies as Your footstool." (Psalm 110:1, HBFV, see also verse 5).
After speaking to them, the Lord was indeed then taken up into heaven, and He sat down at the right hand of God (Mark 16:19, HBFV).
This Jesus has God raised up, whereof we all are witnesses. Therefore, having been exalted by the right hand of God, and having received the promise of the Holy Spirit from the Father, He has poured out this that you are now seeing and hearing (Acts 2:33, HBFV).
Before, however, we delve into the question of who sits to the left of God we should answer why residing on his right is so important.
Authority and Power
Biblically, the right hand symbolizes authority, power, and strength (Genesis 48:14 - 19, Exodus 15:6, Isaiah 23:11, 41:10, 45:1, Revelation 1:16 - 17, etc.). Various studies have shown that at least 70%, and possibly as high as 95%, of all people are right-handed (which means it is stronger than the left one).
Sitting at a person's right side was considered a place of honor. When a newly crowned King Solomon wished to give his mother the highest honor he could he placed her next to him.
Then Bathsheba came in to King Solomon to speak to him for Adonijah. And the king rose up to meet her, and bowed himself to her, and sat on his throne and caused a throne to be set for the king’s mother. And she sat on his right hand (1Kings 2:19, HBFV).
In modern English, we sometimes say that someone is the "right-hand man" of a particular boss or leader. What we mean is that the person has a position of authority that is at least partially derived from the authority of his or her boss or leader. Christ, after his resurrection, stated that God the Father had given him "all authority in heaven and on earth" (Matthew 28:18).
An Empty Seat
In direct answer to your inquiry, the Bible reveals that currently no one is sitting to the left of God. In 32 A.D., just before Stephen became the first Christian martyr, he was granted a rare vision of the very throne room in heaven.
But he (Stephen), being filled with the Holy Spirit, looked intently into heaven and saw the glory of God, and Jesus standing at the right hand of God (Acts 7:55).
Stephen did not see anyone sitting or standing to the left of the Eternal. He certainly did not see the Holy Spirit anywhere near the throne, which one would expect if it really were a person in the Godhead and if the doctrine of the Trinity were true.
What About Lucifer?
Concerning Satan, he at one time covered the Eternal's throne but did not sit next to it (Ezekiel 28:14). When he later stormed the throne of heaven with his demonic hoards (Revelation 12:4), he was not seeking to "share" rule of the universe with anyone. He sought nothing less than to destroy both the Eternal and Christ and take complete control of everything (Isaiah 14:12 - 14)!
A Mother's Request
One day the mother of James and John approached Jesus with a most unusual request.
Then the mother of the sons of Zebedee came to Him with her sons, worshiping Him and asking a certain thing from Him. And He said to her, "What do you desire?"
She said to Him, "Grant that these my two sons may sit one at Your right hand and one at Your left hand in Your kingdom." But Jesus answered and said, "You do not know what you are asking . . ." (Matthew 20:20 - 22).
Was the request by the mother of James and John referring to positions of authority in the third heaven where the Eternal's throne resides?
If James and John flanked Jesus in heaven, whichever one sat on his left hand would separate him from the Father and put him in a position of lesser authority in the universe. This would contradict many scriptures that clearly declare his supremacy of power and rule under the Father (see Matthew 28:18, etc.).
The motherly request was almost certainly referring to the kingdom Jesus would set up on earth to rule humans (often referred to as the Millennium). After all, he did promise the disciples they would sit on thrones judging the twelve tribes of Israel (Matthew 19:28, Luke 22:30). Part of the problem is that those who followed Christ expected his kingdom to be set up during their lifetimes and not in the distant future after their deaths (Acts 1:6).
In conclusion, the Bible reveals that no one sits on God's left hand. This situation is likely to continue into the ages yet to come (see Revelation 22:3).