"My father does not have a younger sister."
Using 一个(yīgè) would specifically state that your father does not have ONE younger sister. In that case maybe you would say "He doesn't have one, he has four!" 我的爸爸没有妹妹 is how you say that he has none at all. Although in English when we use the article "a" it typically means one of something, in this case we mean that he doesn't have any at all.