Definition - What does Acknowledged Child mean?
An acknowledged child is a child whose parents do not deny that the child is their own, and whom they legally and otherwise claim is theirs. Sometimes a male parent will try to deny that a particular child is his to avoid paying child support, etc. Also, he may genuinely think that the child is not his. However, modern science has advanced to provided DNA testing for such issues.
Justipedia explains Acknowledged Child
Acknowledged children are basically just children whose parents do not try to proclaim that the child is not their genetic offspring. For example, if a husband and a wife create a child in wedlock, and they both agree that the child belongs to them, then this would be an acknowledged child, and they both would be legally responsible for the child. However, if a single woman has intercourse with multiple men and conceives a child, the men may deny that the child is theirs. This is where DNA testing could be used to determine the actual father.