Sheriff's chief investigator Tommy Hopkins said deputies received a phone call around 11:45 p.m. Tuesday from a woman who became concerned after she read a message on a friend's Facebook page.
Hopkins said a deputy was sent to a Farmington apartment complex and found the body of 51-year-old Billy Loyd Jr. Loyd's 11-year-old son was found in the same room with a gunshot wound.
Loyd was pronounced dead at the scene. The boy, whose name has not been released, was in critical condition Thursday at LeBonheur Children's Hospital in Memphis.
The investigation is continuing.
"It's such a tragic thing, just a terrible thing," Hopkins said. "We're still looking into it, trying to find a rhyme or a reason."
Hopkins said in the Facebook posting Loyd described his financial troubles, writing that he would soon be evicted from his apartment and he believed his son would be taken from him.
In closing Loyd gave instructions for his and his son's funeral services and advised anyone reading the note to contact the Alcorn County Sheriff's Department, Hopkins said.