Fardereen Deonta Grier was arrested Wednesday after cops were called to a residence outside Atlanta. East Point PD spokesperson Allyn Glover tells TMZ ... when officers responded, Grier was crying and his girlfriend, Destiny Fitzpatrick, was dead in a pool of blood by the front door.

Glover says Grier told cops he was Young Thug's nephew, the son of YT's oldest sister ... but it's unclear why he chose to share the information. A source close to Young Thug confirms the relation.

As for what happened ... we're told Grier first told responding officers he was fending off 2 armed, masked intruders, but officers say he eventually admitted to shooting Destiny in the face. A neighbor allegedly heard arguing in the residence prior to the shooting.

Grier was arrested and charged with murder.

As you know, Young Thug is currently in custody as well ... on a wide range of RICO charges after being denied bond multiple times. His fellow YSL artist, Gunna -- also charged in the RICO case -- was in court Thursday trying to get released on bond, but a judge shot it down.