Ok. I will answer the first question first sense it is the easiest to answer. There are two possible daughters for Joker and Harley. In Batman Beyond: Return Of The Joker, Harley supposedly had two twin daughters named Delia Dennis and Deidre Dennis, or known as Dee Dee. Wait! I just checked and that is wrong. read more
Also note the way he protests that he does not have a daughter and that Joker's daughter is nothing to do with him. (Side note Joker's Daughter is Harvey Dents Daughter. ) Anyway back to Lucy Quinn by Joker denying he has a daughter he is protecting her and keeping her breathing. Joker is not an idiot. He knows even if to Harley he appears not too. read more
The Joker’s daughter is not actually the daughter of the Joker, nor is she the daughter of Harley Quinn. In the current comics, she is a crazy person that found the Joker’s face (he had it removed in one piece). read more
The Joker and Harley Quinn aren’t just partners in crime. They have a four-year-old daughter named Lucy reveals Harley in Injustice: Gods Among Us: Year Two #13 by writer Tom Taylor and artist Bruno Redondo. read more