It's hard to picture Wolverine as a dad. He's growly, quick to anger, and doesn't like to be in one place for too long. Not to mention the fact that he doesn't always know who he is and doesn't like being responsible for anyone but himself. So when Wolverine is tasked with taking care of a young girl, X-23/Laura in Logan, it's fair to say that he's out of his element. But he actually takes to X-23 pretty well. In fact, despite his grumblings to the contrary, it's easy to see that he cares for her, whether he wants to or not. Add that kind of fatherly bond to the mutant genetic similarities between Wolverine and Laura, and there's only one question to ask: is X-23 really Wolverine's daughter?
Some spoilers ahead! Fans of the comics already know that X-23 was created as a kind of female clone of Wolverine. In Logan, the character has a similar origin. Laura was created using Wolverine's DNA and brought to term by a surrogate. It's unclear whether any of her genes came from her surrogate mother or not, but what is clear is that she's not just a clone of Wolverine. (She is a girl, after all.) And, since she's not a clone, then it certainly seems like X-23 is Wolverine's daughter. If nothing else, Wolverine could be thought of as an unwilling sperm donor, if you will.
Professor X seems certain that Wolverine is, in fact, Laura's father. He consistently teases Logan that Laura is "like" him, and not just because she has claws coming out of her hands and the power to heal. Laura didn't just inherit Wolverine's mutant powers, she also got his distrust of outsiders, his knack for violence, and his monosyllabic tendencies. But, for all the evidence that X-23 is Wolverine's biological daughter, Wolverine remains in denial of the entire relationship until the very bitter end.
It's not until Wolverine is — MAJOR SPOILER — about to die that both he and X-23 really embrace the reality of their father-daughter bond. Wolverine might not have been willing to see X-23 as his daughter, but after Logan, he'll always be a father to her.