If a person was nursed by his grandmother, is it permissible for him to marry his paternal cousin?

If your grandmother is the same grandmother of your cousin's daughter who breastfed you, then it is not permissible for you to marry her. Your cousin's daughter becomes like your sister through rada'a (nursing), and nursing prohibits what lineage prohibits, as the Prophet (peace and blessings be upon him) said: "Indeed, nursing prohibits what birth prohibits," and "What is prohibited by lineage is prohibited by rada'a." And the daughters of brothers are unanimously prohibited by lineage, as Allah Almighty says: "Prohibited to you are your mothers, your daughters, your sisters, your paternal aunts, your maternal aunts, the daughters of your brother, and the daughters of your sister."