The first J-frame revolver made by Smith & Wesson was caled the Chief Special (pre model 36). The year was 1950, and the serial numbers started at 1 without a letter prefix. The "no-letter" series of serial numbers went from 1 to 786,544 between the years 1950 to 1969. Serial number 75,983 was made around (but not necessarily in) 1956.
However the practice of stamping a model number (in this case, mod. 36) didn't start until 1957...
So what gives?????
I will speculate, but the only way to find out for sure is to pay S&W a reasonable fee of $30.00 to have Roy Jinks, their historian, go back through the old records (which are in books, not a computer database) and find out what happened.
Anyway, S&W made and serial numbered frames in advance of building them into guns, so it's possible the frame was assembled into a revolver during 1957 or later - in which time it might have been stamped with the "mod. 36" marking.
I would expect the serial number to be stamped on the butt - as they usually were at this time. But there can always be an exception to the rule. The practice of stamping the number on the frame behind the yoke as a regular thing came much later.
The upper (4th) sideplate screw was eliminated at around serial number 75,000 and this gun may or may not have that feature.
This is another case where a photograph could be a big help...