The correct answer is A. EcoRI 5' G^AATTC 3'.
To ligate a fragment cleaved with BamHI into a plasmid cleaved with a different enzyme, the overhangs of both fragments need to be compatible. The BamHI enzyme cuts the DNA at the sequence 5' G^GATCC 3', leaving a 5' overhang of "G".
Among the given options, only EcoRI has a compatible overhang. EcoRI cuts the DNA at the sequence 5' G^AATTC 3', leaving a 5' overhang of "A". The "A" overhang of EcoRI is complementary to the "G" overhang generated by BamHI, allowing for compatible base pairing and successful ligation.
Therefore, the overhang generated by EcoRI (option A) is compatible with the BamHI-generated fragment and can be used for ligation.