In William Faulkner's story "A Rose for Emily", we learn from the townsfolk narrator how Emily's father is, indeed, a huge influence in her life. We know that Emily comes from a traditional and conservative "old school" Southern family in which women are carefully brought into society under the scope of propriety and prudishness.
From what we learn, Emily's father may have gone a bit overboard in overprotecting Emily. We are told that the Griersons may have made themselves appear much higher and mightier than they actually were and, for this reason, they were prone to snubbing everyone else in society. This meant that nothing was good enough for Emily, especially men.
None of the young men were quite good enough for Miss Emily and such. We had long thought of them as a tableau, Miss Emily a slender figure in white in the background, her father a spraddled silhouette in the foreground, his back to her and clutching a horsewhip, the two of them framed by the back-flung front door. So when she got to be thirty and was still single, we were not pleased exactly, but vindicated; even with insanity in the family she wouldn't have turned down all of her chances if they had really materialized.
Therefore, the first sign of the father's influence is that he negatively impacts Emily's ability to create healthy social connections, and to build support systems.
Additionally, Emily's father has made of Emily a seemingly co-dependent person. It is obvious that she only feels safe during the years that he is alive and, afterwards, is too scared to let him go.
She told them that her father was not dead. She did that for three days, with the ministers calling on her, and the doctors, trying to persuade her to let them dispose of the body. Just as they were about to resort to law and force, she broke down, and they buried her father quickly.
This clearly demonstrates that the relationship between Emily and her father is one of complete control in which his alleged protection hinders her own self sufficiency. It does that to such a way that she cannot even let her father go. She will eventually do the same thing with Homer Barron when he threatens to leave her.