In Faulkner in the University, a biographical textbook written by Frederick Landis Gwynn and Joseph Blotner, there is a very illustrative note on how Faulkner himself felt about the character of Miss Emily's father. The character himself is nameless, and there is a good reason for it. He represents a never-ending "presence" and not really an influence per se. Had he been an influence, he could have made a difference in her life, rather than permeated throughout it like a ghost from the past that continuously warns her against the world.
According to Faulkner, Emily had typical and normal hopes and dreams like any other girl would growing up. She wanted what many woman of her society would have wanted: a family where she could be a wife and mother.
However, Mr. Grierson allegedly had Emily "kept down" and "brow-beaten", because he was essentially a selfish man. So selfish that he chose to bypass the needs and the potential happiness of his daughter just for her to eventually take care of him.
he wanted a housekeeper...
Moreover, this pushing over of father over daughter rendered her quite unable to deal with just about anything. She was over-guarded, overprotected and entirely misunderstood as a woman. What is a prisoner to do? Either obey the captor...or manage to escape and live life on her own. Not much of a choice for Miss Emily.
[Miss Emily's father's behavior is]simply another manifestation of man's injustice to man, of the poor tragic human being struggling with its own heart, with others, with its environment, for the simple things which all human beings want. In that case it was a young girl that just wanted to be loved and to love and to have a husband and a family.
Therefore, judging from the way that the father essentially manipulates, traps, and overprotects the daughter, rendering her a social misfit, there is more than enough proof to show that his significance is that of a negative anchor; one that pushes the daughter down to ground her down to his way of life, his rules, and his expectations. Certainly not a good relationship otherwise based on mutual respect and growth.