I keep trying to write it up differently grabbing other points.
If you just follow the scripture out according to the thread title the "children of the promise" it pertains to the gift of the Spirit
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you
in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
The promise is to these as well as all God would call
Acts 2:38 For the promise is unto you, and to your children,
and to all that are afar off, even as many as the Lord our God shall call.
Acts 2:40 And with many other words did he testify and exhort,
saying, Save yourselves from this untoward generation.
Romans 9:5 Whose are the fathers, and of whom as concerning the flesh Christ came,
who is over all, God blessed for ever. Amen.
Romans 9:6 Not as though the word of God hath taken none effect.
For they are not all Israel, which are of Israel:
Romans 9:7 Neither, because they are the seed of Abraham, are they all children:
but, In Isaac shall thy seed be called.
Romans 9:8 That is, They which are the children of the flesh, these are not the children of God:
but the children of the promise are counted for the seed.
That which pertains to Isaac, whereas Paul says,
Gal 4:28 Now we, brethren, as Isaac was, are the children of promise.
And again, ... the children of the promise are counted for the seed (Romans 9:8)
Gal 4:29 But as then he that was born after the flesh persecuted him that was born after the Spirit,
even so it is now.
Gal 4:22 For it is written, that Abraham had two sons,
the one by a bondmaid, the other by a freewoman.
Gal 4:23 But he who was of the bondwoman was born after the flesh;
but he of the freewoman was by promise.
Gal 4:24 Which things are an allegory: for these are the two covenants;
the one from the mount Sinai, which gendereth to bondage, which is Agar.
Gal 4:25 For this Agar is mount Sinai in Arabia,
and answereth to Jerusalem which now is, and is in bondage with her children.
Gal 4:26 But Jerusalem which is above is free, which is the mother of us all.
Gal 4:30 Nevertheless what saith the scripture? Cast out the bondwoman and her son:
for the son of the bondwoman shall not be heir with the son of the freewoman.
Gal 4:31 So then, brethren, we are not children of the bondwoman, but of the free.
John 8:31 Then said Jesus to those Jews which believed on him,
If ye continue in my word, then are ye my disciples indeed;
John 8:32 And ye shall know the truth, and the truth shall make you free.
John 8:33 They answered him, We be Abraham's seed, and were never in bondage to any man:
how sayest thou, Ye shall be made free?
Romans 9:7 Neither, because they are the seed of Abraham, are they all children
John 8:34 Jesus answered them, Verily, verily, I say unto you,
Whosoever committeth sin is the servant of sin. (Romans 6:17, 20, 1 John 3:8)
John 8:35 And the servant abideth not in the house for ever:but the Son abideth ever.
John 8:39 If the Son therefore shall make you free, ye shall be free indeed.
John 8:37 I know that ye are Abraham's seed; but ye seek to kill me,
because my word hath no place in you. (1 John 2:24)
John 8:38 I speak that which I have seen with my Father:
and ye do that which ye have seen with your father. (Ephes 2:3, 1 John 3:8)
John 8:39 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 Abraham.
John 8:40 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. (Gal 4:29, John 15:20)
The children "of the promise" pertains to the Spirit
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you
in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Acts 2:38 For the promise is unto you, and to your children,
and to all that are afar off, even as many as the Lord our God shall call.
And not of the Jews only, but also of the Gentiles, but of them first
Luke 24:49 And, behold, I send the promise of my Father upon you: but tarry ye in the city of Jerusalem,
until ye be endued with power from on high.
Acts 1:4 And, being assembled together with them, commanded them that they should not depart from Jerusalem,
but wait for the promise of the Father, which, saith he, ye have heard of me.
Acts 2:33 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.
1 Cr 12:13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles,
whether we be bond or free; and have been all made to drink into one Spirit.
These being the children of the promise (Spirit)
Christ (even the Son of promise) would send (Luke 24:49)
Now if any man have not the Spirit of Christ, he is none of his. Romans 8:9
The children of the flesh (Abraham through Agar) had come before the Son of promise (Isaac)
Paul writes, Now we, brethren, as Isaac was, are the children of promise. (Gal 4:28)
But as then he that was born after the flesh persecuted him that was born after the Spirit,
even so it is now. (Gal 4:29)
Paul was of the Jews (as one the saying) among the Gentiles, that WE brethren as Isaac was are the children of the promise, that pertains to the Spirit (of promise) in respects to being children of the same (having the Spirit of Christ).