I’ve noticed that the RetroPad button mappings for the Genesis and FBA cores are completely different.
For the Genesis cores, the RetroPad button arrangement for a 6-button controller is:
L1 X R1
Y B A
For the FBA cores, the RetroPad button arrangement for a 6-button game is:
Y X L1
B A R1
I assume this is intentional, and these two tables should be a good reference to set up the Core Input Remapping for one of the two.