Is it permissible for me to marry my paternal uncle's daughter if her grandmother (my grandfather's wife) breastfed her once, given that my paternal uncle's daughter's mother is my father's sister only from the father's side, and the wet nurse is not my grandmother?

If a woman suckles from your grandfather's wife, from milk produced by your grandfather's cohabitation, then there is a difference of opinion among scholars regarding the ruling on the prohibition due to suckling:

- Shafi'i and Ahmad: Prohibition only occurs with five full, satisfying sucklings within the two years (of infancy).

- Abu Hanifa and Malik: A single suckling causes prohibition.

The more preponderant opinion is that of Shafi'i and Ahmad, based on the hadith of Aisha (may Allah be pleased with her) that "ten known sucklings cause prohibition, then they were abrogated by five known sucklings." Therefore, the woman mentioned is not prohibited to you by suckling unless you wish to be precautious.