Should he marry his paternal uncle’s illegitimate daughter?

It is not permissible for the zaani (adulterer) or for any of his sons to marry his illegitimate daughter, and it is not permissible for the zaani or his sons to marry the daughter of the illegitimate daughter. 

This girl is the daughter of your sister through zina, so she is not permissible for you. 

Ibn Qudaamah (may Allaah have mercy on him) said: It is haraam for a man to marry his illegitimate daughter, and his illegitimate sister, and his illegitimate son’s daughter, and his illegitimate daughter’s daughter, and his brother’s or sister’s illegitimate daughter. This is the view of all fuqaha’. End quote from al-Mughni (7/91). 

There is a difference of opinion concerning this issue among the scholars, but this is the vuew of the majority, and it is the most cautious view. 

This does not mean that you are a mahram to this girl and that it is permissible for you to look at her or be alone with her. The fact that someone is haraam for marriage does not always mean that the person is a mahram with whom it is permissible to be alone and so on. 

Ibn Qudaamah (may Allaah have mercy on him) said: What is entirely haraam, namely zina, means that a person is haraam for marriage but it does not mean that a person is a mahram or that it is permissible to look at them. End quote. 

And Allaah knows best.