Yes.Apart from John's reference to " Only-begotten" ( John 1:14,18, 3:16,18, 1 Jn 4:9) ,there is a Biblical evidence that Jesus Christ is the only-begotten son of God.
The following are the exegesis of the church fathers concerning the begetting of Christ Jesus, God's Only-Begotten Son:
In 1 John 5:18, Christ is said to be "begotten" from God and in 1 Corinthians 1:24 it is explicitly said that He is God's Wisdom.
We know that whosoever is born of God sinneth not; but he that is
begotten of God keepeth himself, and that wicked one toucheth him
not. -1 John 5:18 ( KJV)
But unto them which are called, both Jews and Greeks, Christ the
power of God, and the wisdom of God.- 1 Corinthians 1:24 ( KJV)
This idea is found in the Old Testament Scriptures:
In Psalm 110:3 ( LXX)Christ is clearly said to be "begotten" from God. This proves that Christ is begotten from God and Proverbs 8:25 (LXX) speaks of Wisdom as "begotten" from God.
" I have begotten you from my womb before the Morning-Star." - Psalm
"Before the hills, He begets me." -Proverbs 8:25 Septuagint
When we examine the entire Old Testament Scriptures, we will find out that God begot no one except Christ and Wisdom which are in fact one and the same as revealed in the New Testament. This shows that in the Old Testament, God has his "only-begotten" Son, namely, Christ himself, God's Wisdom."
Psalm 2:7 (LXX) is quoted in Hebrews 1:5,5:5 and Acts 13:33 which reveals that Christ is God's "begotten" Son through his resurrection based on Romans 1:4, " declared ( not made)to be God's Son with power according to his spirit of holiness (i.e his godhood)." This proves that Christ is God's only begotten Son before creation because the angels weren't begotten but "made" (Heb. 1:7).
In Colossians 1:15, Christ is said to be "First-born/begotten of all creature" which alludes Proverbs 8:22( LXX) wherein Wisdom said "The Lord created me as the first of his work( activity) , before his works( activities) of old."
It should be noted that there's a big difference between creation ad intra (e.g.begetting) and creation ad extra(e.g. creation ex nihilo). The former is concerned about "begetting" while the latter is about " making."
According to context ( v. 25), Wisdom is said to be "begotten" and hence, it is talking about creation ad intra.On the otherhand, the context of Colossians 1:15 shows that the Son is of same nature with the Father because of his begetting for he is the "image of the invisible God." God's true image is surely invisible, that is,it's distinct yet same like him.
This is the reason why the early church fathers can use the Greek Version of Proverbs 8:22 for proof that Christ is truly God.He is true God because he is God's own true Son, begotten from him not made out of nothing.It proves that he alone is God's only begotten Son because as already said earlier, Wisdom is Christ himself and only him is said to be begotten from God before creation.
In John 1:1, God only has one Word for he only have one mind and in Psalm 45:1(LXX), this Word of him he emitted, produced, begot. It does not mean that God did literally it but rather, it only means metaphorically that he has a specific relationship with his Word as Father to an Only-begotten Son.It's the reason why the word "Only-begotten"[Greek:monogenes] co-existed with the phrase "the Word" [ Greek: ho logos] in the Prologue of John.
Christians are all "born of God" ( John 1:12-13) and hence, they have "divine nature" ( 2 Peter 1:4) but they only have it by "share"(ibid.) unlike Jesus who has it "fully" ( Colossians 2:9).Why is this so? It is because Christians were born of God metaphorically by means of faith (Gal. 3:26)while Jesus' birth from God metaphorically shows equality of nature ( John 5:18, Philippians 2:6).See how harmonious it is that Christ is born of God that's why he has God's very nature and the same thing is true for Christians albeit in reference to salvation in which they are being conformed in the image of the Son (Romans 8:29).Also, because of this truth, it is shown that other sons are "born of God" too and hence, it seems that Christ is not God's "only" begotten Son but do not worry because the Bible itself explains Christ's unique begetting from the Father.John 1:18 says that the One who is in the Father's bosom is the "Only-begotten who is God as to his very nature." [anarthrous monogenes theos= P66, Aleph, B,C - substantival in function].What this means is that although God has other birthed sons, he nevertheless has one only-born Son who equally shares in his nature and that's none other than Christ.
And now, last but not least, John 8:42 offers a very compelling proof for Christ's begetting from the Father:
Here's the context of John 8:42:
38 I speak that which I have seen with my Father: and ye do that which
ye have seen with your father.
39 They answered and said unto him, Abraham is our father. Jesus saith
unto them, If ye were Abraham's children, ye would do the works of
40 But now ye seek to kill me, a man that hath told you the truth,
which I have heard of God: this did not Abraham.
41 Ye do the deeds of your father. Then said they to him, We be not
born of fornication; we have one Father, even God.
42 Jesus said unto them, If God were your Father, ye would love me:
for I proceeded forth and came from God; neither came I of myself, but
he sent me.
43 Why do ye not understand my speech? even because ye cannot hear my
44 Ye are of your father the devil, and the lusts of your father ye
will do. He was a murderer from the beginning, and abode not in the
truth, because there is no truth in him. When he speaketh a lie, he
speaketh of his own: for he is a liar, and the father of it.
The whole subject matter revolves around son-ship and fatherhood which involves the idea of begetting/born. The Jews said that they weren't illegitimate children, that their Father is God but Jesus refuted their claim, that their father is the Devil because they do not believe his word that he is God's very own Son.In verse 42, Jesus said that He proceeded and came from ( Greek: ἐξῆλθον) God as a begotten/born child from a parent. In Genesis 15:4, the Greek word ἐξῆλθον occurs in the context of a real birth in a child to parent relationship. This word always carry the meaning of a real birth in a child to parent context.This begetting is not from Mary but from God himself and verse 58 further supports this when in it Jesus said that "before Abraham became alive, I am already alive."
Notice that Jesus said that he came from God AND was sent from God.The former is about his begetting from the Father before all ages while the latter is about his mission in the economy of salvation.
These are the Bible verses used in proving that Jesus alone is God's begotten Son:
1 Corinthians 1:24 --> Proverbs 8:25 LXX
1 John 5:18 --> Psalm 110:3
Hebrews 1:5,5:5, Acts 13:35 --> Psalm 2:7
Colossians 1:15--> Proverbs 8:22
John 1:1 --> Psalm 45:1
John 8:42 --> Genesis 15:4
All of these Bible verses were used for the Nicene Creed in its affirmation of the Lord Jesus Christ as "Only begotten, begotten before all ages/ begotten not made, of one nature with the Father."