What year did jchiggins make the 583.24 shotgun?

JC Higgins never made shotguns. That is a Sears model number. Shotguns were made by other companies using the Sears brand name- JC Higgins. Yours is likely a High Standard shotgun. If it has no serial number (most did not) it was made prior to 1968. Serial numbers were not required by law until then.