By Roman law, children born to enslaved mothers, by free men or otherwise, assumed the social status of the mother. Children born under these conditions were called Vernae, and as far as I've read, there is no attempt to distinguish between vernae fathered by citizens, freedmen, or other slaves. Although they were born into slavery the title appears to not have been unsavory, and there is funerary evidence that suggests they were treated favorably, in death if not also in life. There area numerous tombstone inscriptions and dedications for vernae, a quick google search can pull up several, and you have to remember that inscriptions are not a cheap date.