Where is Jesus's Soul according to tripartite theology?

You MAY be referring to this passage;

Ephesians 4:7-10, NIV:

7 But to each one of us grace has been given as Christ apportioned it. 8 This is why it[a] says:

“When he ascended on high,
he took many captives
and gave gifts to his people.”[b]
9 (What does “he ascended” mean except that he also descended to the lower, earthly regions[c]? 10 He who descended is the very one who ascended higher than all the heavens, in order to fill the whole universe.)

Now many believe that this passage is addressing the scripture of the rich man and Lazarus in Luke 16 when it says that he also descended "and led captivity captive" referring to Abraham's bosom mentioned in that scripture.

Let me give you a visual aide to define a tripartite being. Many Christians believe God is 3 in 1 (or triune) and according to Genesis, we are/were created in His image. Let's assume this is true for now.

In England during World War II, a renown pastor lived next to a three story home that was bombed and the roof collapsed onto the second floor, the second floor fractured but didn't fall onto the first, but the outside walls cracked. He drew a rather remarkable picture from that event for our creation and loss of standing with God, as well as a restoration, from observing what happened next door.

Assume before being hit, the building was like a human being with the third floor being the spirit, the second being the soul, and first is the body, at our creation. At the point Adam rebelled against God by eating from the tree of good and evil, the relationship between God and man was broken (as evidenced by the third floor collapsing). Because of that collapse, spiritual death as well as physical death occurred, evidenced by the cracks and damage to the second floor and walls (soul and body).

God's interest in his creation, man, is restoring the spirit to have a relationship with Him once again, so He begins to "raise the roof" once again (remember, this is the spirit) which is the relationship between God and Man that was lost at "the fall". The cracked outside walls are not as much of a concern because Paul says, "flesh and blood cannot inherit the imperishable".So, as long as the human is alive, the body (first floor and outer walls) will bear the consequences of "the fall" until that human is "translated" or dies.

Ecclesiastes 12:7, NIV:

7 and the [dust] returns to the ground it came from,
and the spirit returns to God who gave it.

This "building collapse" is NOT true of Jesus because "the fall" had no effect on Him spiritually, only on his flesh (his physical part). Now Jesus stands as the example for us all that there is a spiritual afterlife. Jesus' soul did not leave Him because the soul is thought to be where emotions reside; fear, laughter, joy, love, etc. Since Jesus never lost His relationship with the Father (except at the cross), our understanding of the world is skewed compared to Jesus because that relation to God is broken. So the relation of the soul to the spirit is a link that we probably do not understand well enough. Without the Spirit, our soul looks more like secular humanism and can't understand godly things, though it tries. But that was not the case with Jesus.

The soul is the conscious part of you, and Jesus. His soul went to hell with His Body; returned to the surface of the earth at his resurrection; and to heaven at His ascension:

Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day. Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne; He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption. This Jesus hath God raised up, whereof we all are witnesses. Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear. [Acts 2:29-33 KJV]

Jesus' soul is whever Jesus is.