Thank you for asking a question on This is your Bible.
The phrase CHILDREN OF CHRIST does not appear in the Bible.
That Christ has children is prophesied in Isaiah.
Isaiah 53:10 Yet it pleased the LORD to bruise Him; He has put Him to grief. When You make His soul an offering for sin, He shall see His seed (offspring), He shall prolong His days, And the pleasure of the LORD shall prosper in His hand.
And confirmed in Hebrews.
Hebrews 2:13 And again: "I will put My trust in Him." And again: "Here am I and the children whom God has given Me."
That all who would enter the kingdom of God must be born again by immersion in water and changing the way they think is made clear by Christ.
John 3:3 Jesus answered and said to him, "Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God."
5 Jesus answered, "Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God.
That children are fathered spiritually by the preaching of the gospel is shown by Paul.
1 Corinthians 4:15 For though you might have ten thousand instructors in Christ, yet you do not have many fathers; for in Christ Jesus I have begotten you through the gospel.
Philemon 1:10 I appeal to you for my son Onesimus, whom I have begotten while in my chains,
Those that obey the gospel are born again to a hope of life in Christ.
1 Peter 1:3 Blessed be the God and Father of our Lord Jesus Christ, who according to His abundant mercy has begotten us again to a living hope through the resurrection of Jesus Christ from the dead,
By being baptised into Christ we become spiritual children of Christ and as such become heirs of the promise made to Abraham.
Galatians 3:27 For as many of you as were baptized into Christ have put on Christ.
29 And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise.
The children of Christ are not natural children because he fathered none. The children of Christ are those fathered spiritually by belief and obedience to the Gospel preached by Christ.
By baptism into Christ they become heirs of the promise made to Abraham and spiritual children of God.
John 1:12 But as many as received Him, to them He gave the right to become children of God, to those who believe in His name:
1 John 3:2 Beloved, now we are children of God; and it has not yet been revealed what we shall be, but we know that when He is revealed, we shall be like Him, for we shall see Him as He is.
I hope this helps.