No, there has never been a baby born in space.
While the prospect of space colonization brings up questions about reproduction and childbirth beyond Earth, no human has ever been born outside of our planet's atmosphere. As noted in the provided reference, no one has ever become pregnant in space yet. With the growth of space tourism, pregnancy in space is a possibility for the future, although the effects of space on human reproduction are still being studied. The risks and effects of space travel on pregnancy are currently unknown.
