research dilemma

My family has been researching for many years to find my dad's half brother/sister that was given up for adoption by his dad's (Emery Alvin Byerly) wife (who later annulled the marriage) while he was in jail for a crime that he did not commit. They only put him in jail after his mom died (had a heart attack while chasing him around the washpot) so that they could steal his land. I'm sure that he.she has passed on by now since they were born around 1896, but would love to reconnect with their family. At the time that he/she was adopted out, they were living in the Crittenden County, AR area (small community called Happy). His former wife then moved to Shelby Co, TN with her new husband after the annulment. Do any of you have any information about how that I can proceed to research this?