This is a self-contradiction due to confusion of terms.

10:68

They say [the Christians]: "Allah hath begotten a son!"
Glory be to Him! He is self-sufficient!
His are all things in heaven and on earth!
No warrant have ye for this!

(An essentially identical statement is made in Sura 2:116-117.) This above verse

1) denies that God has a begotten Son, and
2) explains this by saying that God is self-sufficient; he doesn't need anyone to depend on.

10:68 tells us the reason God wouldn't have a begotten Son is because God is self-sufficient. We are going to use a rule from formal logic to make another statement about what this verse tells us. The rule is that (A implies B) is equivalent to (not B implies not A).

IF: It tells us that:

God does not have a begotten Son, for He is self-sufficient.

THEN, according to the Law of Contrapositives, the Qur'an also tells us:

If God HAS a begotten Son, then God is NOT self-sufficient.

Since "not self-sufficient" means the same as "dependent," the above can be restated as:

If God HAS a begotten Son, God is dependent.

This reasoning is very Qur'anic, as we find it this implication clearly spelled out for example in Sura 6:101 (see below).

According to C.S. Lewis, "To beget is to become the father of: to create is to make. And the difference is this. When you beget, you beget something of the same kind as yourself. But when you make, you make something of a different kind from yourself. What God begets is God; just as what man begets is man. What God creates is not God; just as what man makes is not man."

So, what God begets is God; so if God had a begotten Son, it would not mean he would be dependent on some other entity; it would mean that He would be dependent on Himself. DEPENDENT ON HIMSELF. That is the very meaning of self-sufficience. So that verse is obviously self-contradictory and therefore wrong.

The Qur'anic argument receives its force from the reasoning that in order to "beget" God needs a consort, a wife, and would therefore be dependent, i.e. longer self-sufficient. For example, we read in Sura 72:3 "And exalted is the Majesty of our Lord: He has taken neither a wife nor a son." on which Yusuf Ali comments in note 5730: "They abjure ... the doctrine of a son begotten by Allah, which would also imply a wife of whom he was begotten." This is not only the reasoning of the commentators though, since the Qur'an itself gives this argument in Sura 6:101 stating:

Wonderful Originator of the heavens and the earth;
how can he have a son when He has no consort?
He created all things,
and He hath full knowledge of all things.

Obviously, the author of the Qur'an cannot answer this question and and has not the necessary knowledge of all things, since nowhere in the Bible is a wife mentioned. This begotten Son comes from the Father only, without any involvement of a third party, and therefore God was not dependent on anyone. This begetting is a begetting with full self-sufficiency. The author of the Qur'an might not have understood this, but the Qur'anic logic is wrong if it is supposed to be a response to the Biblical revelation.

This topic obviously begs the question what "begetting" means in regard to God, and how there can be still only one God in the "bringing forth" of the Son from the Father. (Note: I did not say "after" but "in" since this is a reality from eternity and not subject to our time frame. The Son was God from all eternity. And this "begetting" is without the involvement of a wife or any sexual act.)