It's a sort of "My Adapt" based on MGSD.
I imagined it as one of the forms it underwent multiple modifications during the battles after the Battle of Edmonton, or as an "if" form it could have had.
The cape is an homage to the one from Metal Build, but I personally chose a tattered feel. I modified the ABC cape that came with the HGUC Crossbone Gundam X-0 and tucked it into the shoulder armor parts.
The boosters on the back of the waist are based on those from Landman Rodi in Option Set 9. It's a Lupus Rex with the legs of Landman Rodi from the Obsequia promotional material attached to its back as boosters.

MGSD Gundam Barbatos Adapt β | 千和's Gunpla works