The Atari 4160 STe is an Atari 520 STe with 4 MB of RAM. It was never marketed and was built by Atari for the developpers. It had a special version of TOS, version 1.6 (the Atari ST Operating System), with less bugs than in the final version !
I own 2x 4160STEs, but as for provenance, they have none, since they have been assembled from parts bought from eBay and other sources. As has been said, a 4160STE is just a 520STE with 4MB RAM. You can even still buy original, NOS 4160STE case badges, so unless you have documentation that proves it to be something special, I wouldn''t take it as read that it''s anything other than an upgraded STE.