Dear Gabriel
If Paternity is Essential, God the son must has it, if else there is some essential thing that Son does not have it, so he can’t be God. So God the son is father as God the father is, So there can’t be any distinction between them.
My problem is not on the Origin.
Paternity is essential because it reveals the beginning of God’s procession of how it relates divine revelation from God the Father through God the Son in God the Holy Spirit.
Paternity does not relate to God’s Essence, Essence apart from Paternity = Father, Begotten = Son, Holy Spirit proceeding is what each “distinct” person of the Trinity is consubstantial.
Paternity distinct from the only begotten, reveals the Father is greater than the Son, not in Essence, but in procession = revelation. Which I introduced to you, that the Father is greater than the Son because the Eternal procession begins in the paternal Father.
It is the procession or revelation of God that reveals the distinct qualities the Father has distinct from the Son. The Father eternally begets the Son, reveals it is from the paternity of the Father who proceeds from no one, begins the procession of God’s presence.
Beginning with the Father or His paternity from which the procession begins God’s revelation in God’s presence not essence.
Another way to look at God’s revelation which eternally proceeds and made present in space and time, deals with the subjects of presence and essence.
What makes the Father distinct from the Son is revealed in the person (al) presence when the Essence of all persons of the Trinity is veiled in each distinct person’s presence. For example the Voice = Father is distinct from the Word = Son, distinct from the breath = Holy Spirit. Each distinct person is fully God in Essence veiled in Presence.
When we can say the Father is not the Son and the Son is not the Father and the Holy Spirit is not the Son or the Father.
Paternity relates to the Father’s presence revealed in the procession of the Trinity which God’s presence revealed to our humanity and creation. The holy Spirit proceeds from the Father and the Son in one spiration of Love.
Do not think that the paternity is revealing a distinct quality of the Father’s Essence, which the Son does not have. Everything the Father has the Son has, because the Father gives everything to the Son except being Father, because the Son does not beget another, or the Son does not begin the eternal procession of God’s revelation, the paternity of the Father begins Gods revelation.
The Father and the Son are consubstantial, not divided, separated or confused. The paternity only relates to the Father’s procession is distinct from the Son’s procession. The Father begins the procession which is His paternity, which does not proceed from no one and from His paternity eternally begets the only begotten Son.
The more we ask questions as you do, and the more we contemplate the mystery of the Trinity, the more our understanding can grow with the understanding that the Trinity is one God and no other, which no one can define God with a definition. The economy of the Trinity of persons reveals God revealing His presence to God’s creation and our humanity, with human terms describing divine revealed spiritual realities in spiritual terms, with the mind of Christ.
Paternity applied to the Father, points to God’s revelation of procession begins from the Father, in and with the Son, whom the Father sends from His Voice in the Word who is God the Son in God’s presence distinct from the God the Father’s presence in procession but who are one God consubstantial in presence One God and no other, never forgetting the Holy Spirit proceeds from both.
Peace be with you