The Free Dictionary has this for its first entry for "father:"
1. A man who begets or raises or nurtures a child.
So, to the dictionary, a father is not only a biological father, but, possibly, a stepfather or foster father who has helped to raise or nurture a child, or, perhaps, even done it himself, with little or no help.
As far as I am aware, there is only one example of foster father- or stepfatherhood in the Bible, but it is a very important one, namely Joseph, Mary's husband, and the earthly father of Jesus.
Joseph did a remarkable thing. He married Mary, even though he knew she was pregnant, and he also knew that he wasn't the biological father of the baby she would bear. (See Matthew 1, which describes the manner in which Joseph discovered this fact.) As the Wikipedia puts it, Joseph is not mentioned much in the gospels, "in which he never speaks." Mary speaks, Jesus speaks to his parents, Joseph is given visions, but the Wikipedia is correct -- he never speaks. We have to infer his reaction.
God entrusted Joseph with important aspects of the care of His own Son. Matthew 2 tells us that it was Joseph, not Mary, who was divinely warned to flee to Egypt, and was told to return from Egypt.
Joseph is a great example of an apparently humble man, who did what he needed to do for his foster son, even, apparently, not telling others that Jesus wasn't his son. (Luke 3:23)
In this day and time, a lot of stepfathers, and foster fathers, have stepped up, as it were. They are doing a good, humble, patient job of raising and nurturing daughters and sons that aren't their biological offspring. God bless them, and help them.
Sunspots: A Google search for the words wicked stepmother returns about 169,000 web pages. A similar search for the words wicked stepfather returns less than 92,000. I can't think of a single fairy tale that has a wicked stepfather as a character, but there are several with wicked stepmothers. Why? I don't really know.
I work a little with elementary school children. I ran into a case in which a boy, about 10 years of age, was downright obsessive about his biological father. He told me that his stepfather was a good father, good to him. From what I could gather, his biological father was not -- he had not contacted the boy for months, including at Christmas and his birthday. Yet he was somehow longing for his "real" father, almost all the time. God help him, and others like him, and help fathers (and mothers) to be better at carrying out their responsibilities.
The Wikipedia article on Joseph says that the word τεκτων (Anglicized as tekton, which is probably related to the modern technician.) is used to describe his occupation. (Matthew 13:55). This word, it says, "cannot be translated narrowly; it evokes an artisan with wood in general, or an artisan in iron or stone." That same word is used to describe Jesus, Himself, in Mark 6:3.
Thanks for reading. If any fathers read this, be a good father, God helping you (and me). If any children of stepfathers or foster fathers read this, be sure to let them know how much you appreciate them.