There are four verses in the New Testament (KJV) which contain the phrase “God and the Father”. They do not say that “God” and “the Father” are two completely different persons (or deities). They are, in fact, some of the verses that implicitly teach the Trinity of God. (He is Father, Son, and Holy Spirit – three in one.) Quoting from the KJV, the verses are:

Eph. 5:20 Giving thanks always for all things unto God and the Father in the name of our Lord Jesus Christ.

Col. 1:3 We give thanks to God and the Father of our Lord Jesus Christ, praying always for you,

Col. 3:17 And whatsoever ye do in word or deed, do all in the name of the Lord Jesus, giving thanks to God and the Father by him.

James 1:27 Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world.

In all four cases, the phrase is translated from the Greek “θεῷ καὶ πατρὶ” . All the Greek text and manuscript sources (used for the KJV) contain the phrase. The word “and” comes from the Greek word “καὶ”.

Other translations say “God, the Father”, “God the Father”, “God, even the Father”, or “God our Father”, omitting the word “and”.  Those translations include the NASV, NIV, HCSB, NLT, and the NKJV.

There are some exceptions:  Col. 1:3 in the NKJV says “the God and the Father”.  James 1:27 in the NASV and HCSB say “our God and Father”.  The NKJV matches the KJV in James 1:27.

Some of the Greek sources used by the newer versions do not include the word “καὶ”.  They say simply
“θεῷ πατρὶ“.  Those sources only apply to the verses in Colossians.  All the sources for Ephesians and James contain “καὶ”.

The word “καὶ“, of course, is often used simply to conjoin unrelated items.  An example is Matt. 2:11, which contains the phrase “ . . . gold, and frankincense, and myrrh”.  However, the word is also used in some cases to explain or add specification to the proceeding word.  That is exactly what the “and” does in the KJV verses above. They could say “God, specifically, the Father” and have the same meaning.  If the “and” is simply removed, as other versions do, it also yields a good translation.

There are instances in the KJV (as in other translations) where a different word is used in place of “and”.  One common substitute is the word “even”.  Here is an example:

II Cor. 1:3 Blessed be God, even the Father of our Lord Jesus Christ, the Father of mercies, and the God of all comfort;

Eph. 5:20 (mentioned above) as translated in the NASV uses the same substitution:

Eph 5:20 (NASV) always giving thanks for all things in the name of our Lord Jesus Christ to God, even the Father;

Here are some other examples; in each case the highlighted word(s) are translated from “καὶ”:

II Cor. 1:8 For we would not, brethren, have you ignorant of our trouble which came to us in Asia, that we were pressed out of measure, above strength, insomuch that we despaired even of life:

II Cor. 3:5 Who then is Paul, and who is Apollos, but ministers by whom ye believed, even as the Lord gave to every man?

Romans 1:13 “Now I would not have you ignorant, brethren, that oftentimes I purposed to come unto you, (but was let hitherto,) that I might have some fruit among you also, even as among other Gentiles . . .”.

At least one verse in the KJV actually deletes the word “and”.  An example is II Cor. 1:13. Notice the highlighted conjunction “or”:

II Cor. 1:13 For we write none other things unto you, than what ye read or acknowledge; and I trust ye shall acknowledge even to the end;

Here's how it reads with the "and" left in:

II Cor. 1:13 For we write none other things unto you, than what ye read or and acknowledge; and I trust ye shall acknowledge even to the end;

Manuscript sources cited below include:
Aleph(א) (codex Sinaiticus),
A (codex Alexandrinus),
B (codex Vaticanus), and
Byz (the Byzantine manuscripts).

For Col. 1:3, the only source using “θεῷ πατρὶ“ is B.
       Those using “θεῷ καὶ πατρὶ“ are א, A, and Byz.
For Col. 3:17, sources using “θεῷ πατρὶ“ are א, A, and B.
       The only source using “θεῷ καὶ πατρὶ“ is Byz.
For the verses in Ephesians and James, all the sources use “θεῷ καὶ πατρὶ“.