dr43sizwiz,
Welcome to our forum. If your gun is truly c.1957 it will have 4 screws in the sideplate including the one under the right side grip.
Also, there will not be a serial # on the rear face of the cylinder.
The 6 serial # locations left after WW II are:
Gun butt* - or forestrap* on I frames with grips that cover the butt
Barrel - bottom of barrel or in extractor shroud
Yoke - on rear face visible thru a chamber with a flashlight
Extractor star - backside
Cylinder - rear face
Right stock – backside
Eventually getting down to only 3 serial # locations left by c. 1957 which are:
Gun butt* - (or forestrap* on I frames with grips that cover the butt)
Extractor star - backside
Right stock – backside
Other multi-digit numbers that are in the yoke cut on the frame (or left side of grip frame once the serial #/Mod # were stamped in the yoke cut), on the yoke opposite, and on the inside of the sideplate are factory ‘work’ numbers, still used to this day, long after serial number locations decreased.
*NOTE: The one TRUE place you can be sure of reading the serial number, including letter prefixes, is the BUTT of the gun, (or Front grip strap on non-round butt .22/32 & Regulation Police pre Model of 1953 I frames).