On what basis did Mormon Prophet Joseph Smith declare that God the Father, the Son and the Holy Spirit cannot indwell a believer? The following is what Joseph Smith said from &quot;Doctrines &amp; Covenants, Section 130, Paragraph 3 regarding John 14:23.

John 14:23—The appearing of the Father and the Son, in that verse, is a personal appearance; and the idea that the Father and the Son can dwell in a man’s heart is an old sectarian notion, and is false.&quot;

Here is what the verse says

John 14:23,&quot;If anyone loves Me, he will keep My word, and my Father will love him, and We shall come to him, and make Our abode with him.&quot;

The &quot;we&quot; of &quot;we will come unto him&quot; refers to the Father, the Son and the Holy Spirit. In other words, the disciple becomes the residence of God. the Apostle Paul elaborates on this truth when he says, &quot;Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you?&quot; 1 Corinthians 3:16.
Paul also said, &quot;Or do you not know that your body is a temple of the Holy Spirit who is in you, whom you have from God, and that you are not your own.&quot; 1 Corinthians 6:19.
Other verses would include 1 John 4:15, &quot;Whosoever confesses that Jesus is the Son of God, God abides in Him, and he in God.&quot; Ephesians 3:17 and Revelation 3:20 also support God making His abode in believers.
It is my opinion on this is since Smith and his followers believe that God has a body of flesh and bone and cannot be everywhere present at the same time therefore God cannot indwell a believer.
I decided to look up the word &quot;sectarian&quot; that Smith used. &quot;Denoting or concerning a sect or sects.&quot; Is not this the question that Smith asked God the Father and God the Son? &quot;Which of all the sects was right that I might know which to join.&quot;
The answer he received was,

&quot; I must join none of them, for they were all wrong; and the personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; that they draw near to me with their lips, but their hearts are far from me; they teach for doctrines the commandments of man, having the form of godliness, but they deny the power thereof.&quot;

So my question is:
On what basis did Mormon Prophet Joseph Smith declare  that God the Father, the Son and the Holy Spirit cannot indwell a believer?
I meant to post Romans 8:11 but simply forgot. &quot;

But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ Jesus from the dead will also give life to your mortal bodies THROUGH HIS SPIRIT WHO INDWELLS YOU.&quot;

The following is the LDS view of the Holy Spirit, https://www.churchofjesuschrist.org/study/manual/gospel-topics/holy-ghost?
lang=eng
Notice the statement:

All honest seekers of the truth can feel the influence of the Holy Ghost, leading them to Jesus Christ and His gospel.&quot;

The Dictionary defines &quot;feelings,&quot; Feeling is a general term for a subjective point of view as well as for specific sensations; readily affected by emotion.
The point is that &quot;truth&quot; is not based on subjective feelings or emotions.
On what basis did Mormon Prophet Joseph Smith deny that God the Father, the Son and the Holy Spirit cannot indwell a believer?

As others have pointed out in the comments, Joseph Smith did not say that the Holy Spirit cannot indwell a believer, only that the Father and the Son cannot.  Doctrine and Covenants 130:3 that you quoted says &quot;the idea that the Father and the Son can dwell in a man’s heart is an old sectarian notion, and is false.&quot;  No mention is made here of the Holy Spirit.
With that established, your supposition

It is my opinion on this is since Smith and his followers believe that God has a body of flesh and bone and cannot be everywhere present at the same time therefore God cannot indwell a believer.

seems a reasonable explanation for why Joseph Smith would teach that the Father and the Son (both held by Joseph Smith to be embodied Beings) cannot dwell in a person's heart.
Off the top of my head, I cannot think of any other scripture that could be used as a basis for this, other than the passages (including Joseph Smith's own accounts of seeing the Father and the Son) stating further that the Father and the Son have bodies.  I would welcome any additional exposition people have to add to my answer.