Who does Fagin think Nancy wants to meet on Sunday night in Oliver Twist?

Fagin thinks that Nancy is cheating on Bill.

Fagin knows that Nancy is mistreated by Bill Sikes. As a woman, she is particularly vulnerable in this criminal lifestyle. She stays with Bill for protection more than out of love. He beats her and berates her. Therefore, when Nancy wants to leave, Fagin assumes she has taken another lover who treats her better than Bill.

He had conceived the idea—not from what had just passed though that had tended to confirm him, but slowly and by degrees—that Nancy, wearied of the housebreaker's brutality, had conceived an attachment for some new friend. (Ch. 44)

This is actually not true at all. Nancy has a new friend all right—Oliver. She is looking out for him. Nancy risks her life to try to protect him and help him. Oliver has a good heart and she knows it.

Nancy is meeting with Rose Maylie, concerning Oliver. She knows that he does not belong on the streets or with Fagin, and should be with his family.

'Every Sunday night, from eleven until the clock strikes twelve,' said the girl without hesitation, 'I will walk on London Bridge if I am alive.' (Ch. 40)

Nancy knows that it is dangerous for her to sneak out and meet Rose like this. Bill is supremely jealous, and will likely come to the same conclusion that Fagin did. Also, the perhaps larger risk is that Bill or Fagin will think that she is meeting with the police to “peach” on them, or tell on them.  Either way, one or the other will assume that she is betraying them. This is why Bill kills Nancy.

In some ways, Nancy is betraying them. After all, Oliver is business. Their job is to keep him and turn him into a criminal. She should not be trying to protect him or rescue him if she is loyal to Fagin or Bill. However, in spite of the fact that she is a “fallen woman,” Nancy is a good person. It is too late for her, but not too late for Oliver.