Is it permissible to marry my maternal cousin if his sister was nursed by my maternal grandmother along with my maternal aunt, knowing that I was not nursed by his mother and he was not nursed by my mother?

Suckling establishes what is forbidden by lineage. Thus, what is forbidden by lineage is also forbidden by suckling. The prohibition is specific to the suckled child, not their siblings, making them a child to the woman who provided the milk and her husband. Based on this, your fiancé's sister suckling from your grandmother does not make him one of your mahrams, and it is permissible for you to marry him unless he suckled from your mother, or you suckled from his mother, or you both suckled from another woman. For suckling to be prohibitive, there must be five definite, satiating sucklings.