When the .357 Magnum was first issued, S&W hyped its super power (like the .44 Magnum later) and part of the hype was the addition of a special number (the Registered Number) stamped on the frame under the yoke, and an accompanying certificate with the same number. The registered number was not the serial number, which was applied in the normal places. Some 5500 registered guns were made.
The certificate was issued to the first purchaser, and had his (I know of no women certificate holders) name and home town, as well as the trigger pull weights (SA and DA), and the range the gun had been targeted at (AFAIK, always 25 yards, with a 6 o'clock hold).
Registered Magnums were not specifically custom guns, although they had to be specially ordered and options could be ordered as with all S&W revolvers of the time. They were specially tuned, but there were no "registered Magnums" as distinct from "regular" Magnums; all .357's were "Registered Magnums" up to about 1939, when the registration practice and marking was discontinued as both too expensive and too time-consuming due to the increased demand for the .357, plus the factory gearing up for war contracts.
A LNIB registered Magnum with certificate can run to well over $12K, much more if the certificate was issued to a celebrity, but be warned that both the number and certificate have been counterfeited, so both a serial number check and an S&W letter would be advisable before purchase. (.357 Registered Magnums were serialized in the N frame series, so there is no "block" of .357 serial numbers.)