When he emptied himself of all His right to the powers that are God?
What was left? His human Soul.
The seed of the Father you speak of is not mentioned in Scripture. It does sound good... But it is not Scripture.
What we have is the "seed of the Holy Spirit."
Jesus said to Nicodemus that what is born of the flesh is flesh, and what is born of the Spirit is spirit.
Our human spirit is what the Spirit "begets" in us. That being... our 'human spirit.'
Flesh gives birth to flesh, but the Spirit gives birth to spirit." John 3:6
At regeneration the born again believer becomes body, soul, and human spirit."
The human spirit is not to be mistaken for the indwelling Holy spirit.
For we have become body, soul, and human spirit.
May the God who gives us peace make you holy in every way and
keep your whole being—spirit, soul, and body—free from every fault
at the coming of our Lord Jesus Christ." 1 Thes 5:23
For the Church age believers? Not the OT believers. We receive an additional gift when born again.
That new gift is the Indwelling Holy Spirit which is not to be confused for our human spirit that all receive at regeneration.
The Spirit himself testifies with our spirit that we are God’s children." Romans 8:16
grace and peace......