I re-watched an episode of the Newsroom (Season 2, Episode 2 if you have HBO Max) which discussed the case. Here is a short YouTube clip from CNN, the day before Mr. Davis' execution.
Here is a portion of the Georgia Dissenting (Minority) opinion:
We have noted that recantations by trial witnesses are inherently suspect, because there is almost always more reason to credit trial testimony over later recantations. However, it is unwise and unnecessary to make a categorical rule that recantations may never be considered in support of an extraordinary motion for new trial. The majority cites case law stating that recantations may be considered only if the recanting witness's trial testimony is shown to be the “purest fabrication.” To the extent that this phrase cautions that trial testimony should not be lightly disregarded, it has obvious merit. However, it should not be corrupted into a categorical rule that new evidence in the form of recanted testimony can never be considered, no matter how trustworthy it might appear. If recantation testimony, either alone or supported by other evidence, shows convincingly that prior trial testimony was false, it simply defies all logic and morality to hold that it must be disregarded categorically.