Oooh, so close. Ripley had a daughter. They cut the scene about that in the second movie when they edited it down for The shorter cinematic runtime. Much like Terminator 2, the director's cut which reincludes such content makes the movie much better.
Spoiler:
In the case of the movie Alien, Ripley finds out her daughter died of old age, and it serves as a plot point to build up why she gets so rapidly and heavily attached to Newt later on.
Not newt, she has an actual daughter. Amanda. Ripley spends so much time lost and in cryo sleep that her daughter lives an entire life and dies two years before Ripley gets back. In Aliens Newt serves as a surrogate for Ripley's daughter and the manifestation of her guilt for missing her entire life.