What is the ruling on a woman marrying her paternal cousin if her father believes he was nursed by the woman's paternal aunt (the husband's mother), while the paternal aunt's daughters deny this nursing ever occurred?

If your father confirmed that your paternal aunt nursed him five full, satisfying sucklings before he was two years old, then that establishes fosterage according to the Hanbalis. However, the majority of scholars do not establish it based solely on the nursing woman's report. If your father did not confirm her report, then fosterage is not established, neither according to the Hanbalis nor others. Fosterage is accepted based solely on the nursing woman's testimony according to the Hanbalis, whereas the Shafi'is and Malikis stipulate her testimony being accepted along with others. The Shafi'is stipulated that the nursing woman should not demand payment for her testimony to be accepted. Testimony regarding fosterage is only accepted if detailed (mentioning the time and number of sucklings). If doubt arises concerning the existence of fosterage or the number of prohibited sucklings, then prohibition is not established. Accordingly, if your father did not confirm the report, then your marriage is valid. If he did confirm it, then your marriage is valid according to the majority of scholars and invalid according to the Hanbalis.