It can refer to the First Person of the Trinity, in relation to the Second Person who is His "only-begotten" Son. This is a relationship which is singular and unique.
It can refer to God in His relationship to "all who believe," and thus take in many people as His children, but not all, as you said, dmanLA.
It can refer likewise to God in His relationship to all who are made in His image and likeness, which is a way of expressing paternity:
Then God said, "Let us make man in our image, in our likeness.."(Genesis 1:25)
"When Adam had lived 130 years, he had a son in his own likeness, in his own image..."(Genesis 5:3)
That's to say, the whole human race, as here:
Ephesians 3:14-15
"For this reason I kneel before the Father,
from whom every family in heaven and on earth derives its name."
This conveys the same idea as Acts 17:25-26:
"...He giveth to all life, and breath, and all things; And hath made of one blood all nations of men for to dwell on all the face of the earth."
Thdse are three different meanings of the word "Father": not with exactly the same meaning, not identical, but overlapping.
According to the Koran Alexander the Great was a Muslim !
Which would have been news to him since he thought he was the son of Zeus (or so his mother told him!)