There were a number of replacement floppy controllers during the XT/AT early 386 era, such as the Sysgen Omnibridge, the Micro Solutions Compaticard, etc. There were also "switch" type adapters that could expand your 2-drive controller to 4 drives by providing support for extra drive select and motor enable outputs. Many had options to provide +5 and +12 volts via unused lines in the DC37 connector. Unhappily, there was no standard for these; the Micro Solutions cards even included jumpers to configure the output to the power pins to match an existing drive.
Bottom line is that you're going to have to open the box and buzz out the power lieads to the connector. to figure out what you've got--and then decide what you'd like to do about it. The 5150/5160 floppy adapter does not supply power via its DC37F.