If you must use the term "Begotten God" from a different translation of John 1:18 then use it correctly as follows.
"No one has ever seen God; the only begotten God, who is in the Father’s bosom, he has made him known."
That provides further support for the notion that the Father’s eternal begetting of the Son places the Son in possession of the full divine nature, so that it may rightly be said that the Son is “true God of true God the Father".
