Can he marry the daughter of his mother’s paternal uncle?

Praise be to Allah.

A person’s paternal uncle is the paternal uncle of all his offspring, because the paternal uncle is the brother of the father or grandfather. So the mother’s paternal uncle is regarded as a paternal uncle to her children, and his children are paternal cousins to the children of that mother. Although in some cultures they call them maternal uncles and aunts, this is just a custom that is followed among some people; it does not carry any weight in terms of sharee‘ah or linguistically.

Based on that, the daughter of the mother’s paternal uncle is regarded as your paternal cousin, and the daughter of a paternal uncle is not a mahram, so there is nothing wrong with you marrying her.

See the answer to question no. 34791