First, the word "son" does not occur in John 4:26 nor in the immediate surrounding verse. Therefore, Jesus was NOT claiming to be God's Son.

However, what Jesus did claim was two things:

• that He was the great "I Am"
• that He was also the Messiah of the OT prophets in answer to the woman's statement

That is, Jesus uses the unpredicated "ego eimi" as both a statement of existence and identification as He does on 14 other occasions in the NT - see appendix below.

The same unpredicated "I Am" occurs in the LXX and always refers to YHWH in the OT and is used in the same two ways:

• a claim to be the "I Am" of YHWH as stated in Ex 3:13-15, and
• I claim of self identification as God

APPENDIX - Unpredicated "I Am" in the NT

It is better to understand this "I am" statement in a larger context. Let us examine the unpredicated use of the exact phrase ἐγώ εἰμι, in the NT.

• Matt 14:27, Mark 6:50 – “Be encouraged. I am.” [To the frightened disciples in the boat.] That is, Jesus claimed to be the source of their safety as God is.
• Mark 13:6, Luke 21:8 – “Many will come in my name saying, ‘I am’”.
• Mark 14:62, Luke 22:70 – “Jesus replied, ‘I am’”. [He was then accused of blasphemy by the Jews and condemned.]
• John 4:26 – “Then Jesus said, ‘I am.’” [To the Samaritan woman at the well. Here Jesus uses the "I Am" to confirm He is both the Messiah and the I Am of the OT.
• John 6:20 – “But then [Jesus] said to them, ‘I am. Fear not.’” [To the frightened disciples in the boat.] This assured them that Jesus was their source of safety because Jesus was the I Am
• John 8:24 – “If you do not trust/believe that I am, you will die in your sins.” Jesus, as the I Am is the source of salvation.
• John 8:28 – “When you will lift up the Son of Man, then you will trust/know that I am.” Jesus, as the I Am is the source of salvation.
• John 8:58 – “Truly, truly, I say to you; before Abraham existed, I am.” [The Jews then tried to stone Him for blasphemy.] Note that this and the previous two mean that Jesus, in the space of this chapter of John 8 uses the unpredicated “I am” idea in the present (v24), future (v28) and past sense (v58). V24 & 28 appears to be tied to believers’ salvation as well.
• John 9:9 – “Some were saying that, ‘this is [that one]’, and others were saying ‘no, it is like him.’ But he was saying, ‘I am [that one].’” (This instance is clearly identification rather than existence.)
• John 13:19 – “From now [on] I tell you before the occurrence, that you may believe when it occurs that, I am.”
• John 18: 5, 6, 8 – “He said to them, ‘I am.’ …Therefore, when He told them, ‘I am’, they fell backward to the ground.” [This occurred when the Jews tried to arrest Jesus in the garden. It could be reasonably argued that this is a case of identification. However, the fact that the arresting mob fell backward suggests that much more is intended here.]

It is interesting that, according to Mark 13:6 and Luke 21:8, one of the distinguishing characteristics of false christs is their claim to be “I AM”. Unfortunately, there has been a historical parade of charlatans making such false claims.

Thus, with the obvious and rather trivial exception of John 9:9 (and self-exclusory Mark 13:6 and Luke 21:8), all of the “I am” existence statements in the New Testament, including the 7 in John, were spoken exclusively by Jesus, and all were either the basis for absolute trust/belief and reassurance in Jesus, or were a clear declaration of His claim to be the “I AM.”

These unpredicated "I am" claims of Jesus are clear allusions to the same phenomenon in the LXX of the OT, namely, Deut 32:39, Isa 41:4, 43:10, 13, 25, 45:19, 46:4, 48:12, 51:12, 52:6. In these cases, YHWH is using the name He specified in Ex 3:13-15 as,

God said to Moses, “I AM WHO I AM. This is what you are to say to the Israelites: ‘I AM has sent me to you.’” … This is My name forever, and this is how I am to be remembered in every generation.