Can he marry his paternal cousin’s daughter?

Praise be to Allah.

Yes, it is permissible for you to marry the girl mentioned, who is the daughter of your paternal aunt’s son and the daughter of your paternal uncle’s daughter, because she is not your mahram. ‘Ali (may Allaah be pleased with him) married Faatimah (may Allaah be pleased with her), the daughter of the Prophet (peace and blessings of Allaah be upon him), and she was the daughter of the son of his paternal uncle. 

The daughters of your paternal uncles and aunts are permissible for you to marry, and so are their daughters, no matter how far the line of descent extends. And the daughters of your maternal uncles and aunts are also permissible for you to marry, and so are their daughters. Perhaps you are confused because it is customary for such girls to call you uncle, but this is just a custom, and it does not mean that it is haraam to marry them. 

For more information on marrying relatives, please see the answer to question no. 72263. 

May Allaah help us and you to do that which He loves and which pleases Him. 

And Allaah knows best.