Is my paternal cousin considered a legitimate brother to me and my sisters if he nursed from my eldest sister on my father's side?

If the woman who breastfed your cousin is your father's wife, and the milk was produced as a result of your father's intercourse, then your cousin becomes your father's son, and you become his paternal siblings. This is known as the prohibition due to the milk of the male, and it is supported by the hadith of Aisha (may Allah be pleased with her) in Sahih al-Bukhari. However, if the woman who breastfed him was a foreign woman, then your cousin is not your brother, but rather he is only a brother to whoever else was suckled by that woman with him.