There are two possible fathers of Georgia's baby from the Netflix show "Ginny & Georgia" as of the end of Season 3: Mayor Paul, her then-husband, and Joe, the Blue Farm Café owner who has feelings for her. The show's creator has confirmed that they know who the father is but keeps it flexible and open to change. The characters' relationships and circumstances make both men plausible fathers, with the storyline leaving it ambiguous for now.
Separately, there is a real-life case in Georgia involving a woman named Adriana Smith who was pregnant and declared brain-dead. She was kept on life support for several months so that her fetus could develop until delivery. This is unrelated to the "Ginny & Georgia" storyline regarding Georgia's pregnancy and the baby's paternity.
In summary, for the fictional character Georgia's baby, the father could be either Mayor Paul or Joe, with the storyline not definitively revealing this yet.