You're correct, with maybe one exception (see John 10:34-36 below). Both Yeshua and Paul define the 'one true God' to be the Father:
John 17:3
.. And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent, ..
1 Corinthians 8:4-6 (here Paul refers to the 'Shema' in Deuteronomy 6:4)
... we know ... there is no God but one,
For although there may be many 'gods' and many 'lords' -
yet for us there is one God, the Father, from whom are all things and for whom we exist,
and one Lord, Jesus Christ, through whom are all things and through whom we exist.
Ephesians 4:5-6
.. one Lord, one faith, one baptism, one God and Father of all, who is over all and through all and in all.
1 Thess 1:9-10
.. to serve the living and true God, and to wait for his Son from heaven ..
Even in the TNK/OT you find YHWH is the God of the Messiah:
Micah 5:3/4-4/5 (about the Messiah)
And he shall stand and shepherd his flock in the strength of YHWH,
in the majesty of the name of YHWH his God.
Yet; the word 'god' (elohim (Hebrew) / theos (Greek)) is also used for others than YHWH, Yeshua himself refers to that in John 10:34 (replying to the accusation of blasphemy). Yeshua quotes Psalm 82:6 and his reply clearly indicates He interprets the word 'elohim' there to refer to human beings:
John 10:34-36
Jesus answered them, “Is it not written in your Law, ‘I said, you are gods’? If he called them gods to whom the word of God came —and Scripture cannot be broken— do you say of him whom the Father consecrated and sent into the world, ‘You are blaspheming,’ because I said, ‘I am the Son of God’
Yeshua's statement supports the notion the word elohim/theos/god is broader in use/meaning than just a reference to the 'one true GOD' / the Father. That's why John 1:1c can state
'and the word was with god and god was the word' (capitals intentionally omitted to reflect the basic Greek and original word order).
