Kate gives Cassidy an envelope full of cash that is from Kate's settlement with Oceanic. Kate also tells her the truth about what happened after the crash. Sawyer told Kate where to find Cassidy and to take care of Clementine, who's apparently asleep in her crib. That would place Sawyer's relationship with Cassidy not long before the crash and not long after he was released from prison. Kate tells Cassidy that she told her the truth because she though Clementine deserved to know that her father cared about her. Kate then tells her about Sawyer jumping from the helicopter and Cassidy calls him a coward for it. Cassidy says that he jumped to get away from Kate. Cassidy goes on to ask if Aaron is Sawyer's son. Kate tells her that she was pregnant before she met Sawyer. Cassidy quickly realizes she's lying and that the baby is not hers. Kate says she's lying about Aaron "because she has to."
Nothing too deep to delve into here. The biggest thing of interest is how close the timeline in which Sawyer meets Cassidy and gets her pregnant, when she turns him in and he goes to prison and when 815 crashed. If in 2005, Clementine is still a baby, all of those events happened pretty close together. Sawyer was a busy guy.
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