These next two chapters will make the most sense if you've read The Han Solo Trilogy (The Paradise Snare, The Hutt Gambit, Rebel Dawn) by A.C. Crispin. For anyone who has not read those books, here is a quick summary:
The Han Solo Trilogy deals with Han Solo's life before Episode 4. It begins when he is seventeen years old, and stretches over a ten-year time span. In the first book, Han meets Bria Tharen, a slave on the planet Ylesia. Han rescues her, and the two go to Corellia to meet Bria's parents. They do not care for Han, and Han and Bria leave to go to Coruscant, where Han is going to withdraw the funds of his bank account. Something goes wrong, and he nearly gets arrested. Bria and Han spend one last night together, and Han wakes up the next morning to find Bria gone. She left him to join the rebellion.
About ten years later, Bria approaches Han and asks him to help her in a mission for the rebellion. Han at first blows her off, still quite sore after being dumped ten years prior, but later reconciles and agrees to help her. She and the rebels plan to raid a treasure room, and promise Han and his smuggler friends a cut for helping. Han and Bria get back together, but when they reach the treasure room, the Rebels turn their blasters on the smugglers. Han ad his friends leave mostly empty handed, and all the smugglers hate Han. (This is why Lando calls Han a "double crossing no-good swindler" in Episode 5.)
"Your father?" Leia was surprised, with good reason. Han had never mentioned having any children. She shot a glance at him. He was staring at the floor, refusing to meet her eyes. She turned back to Jara. "How- is that possible?"
Jara snorted, and gestured at Leia's bulging stomach. "I assumed you knew. You see, when a man and a woman meet"-
"She gets it," Han snapped. "What she was referring to was the other half of your parentage."
Jara raised her eyebrows. "You don't know?"
"Should I? I didn't even know I had a child until now."
Jara nodded sadly. "Figures," she muttered. "That schutta lied."
Cautiously, Leia asked, "Who is your mother?"
Jara looked at her, then at Han. "Bria. Bria Tharen."
Han sucked in a breath. Memories came flooding back. A beautiful Corellian woman, a beach, a hotel on Coruscant, desperation, a letter… then seeing her again, years later. She had seduced him- or maybe he had seduced her- and she had betrayed him.
"That's not possible," Han replied. "She died months after we"- he glanced at Leia. "You know."
Jara snorted. "Spare me the details. Well, what about the first time?"
Han's eyes widened. "You mean"-
"I was already alive and kicking when you hooked up the second time? When she left for Nar Shaddaa, she told me that you abandoned her to go join the Imperial Navy. That we were only holding you back."
"That's ridiculous! She was the one who left! She abandoned me! I was devastated"- He stopped. Leia was walking out of the main hold. "Leia!"
Then he heard a click. "Stop right there. If I have to listen to this, so do you."
"Jara"- something caught in Han's throat. "Don't do that."
Something flickered in her eyes. She lowered her blaster. "Forget it. At least they can have a father." Then she put the blaster in her holster, and walked out of the Falcon.