The old Sharps cartridges utilized jacketed bullets, but the jackets were paper.
The earliest jacketed handgun bullets that I know of were the soft point bullets for the earliest autoloaders. In his famous treatise Sixguns By Keith Elmer Keith denounced jacketed handgun bullets very soundly.
The high velocity loadings of the .38-40 and .44-40 were loaded with jacketed soft point bullets, these appearing maybe around the turn of the last Century, 1900 or so. When the .44 Magnum was introduced in 1955 it opened up a whole new era for jacketed handgun bullets. Some of the earliest bullets by the late Jim Harvey were half jacketed bullets, really sort of an enlongated gas check. Speer produced these for awhile, using pure lead cores swaged into a SWC profile. Then came the jacketed bullets with the ogives with which we are familiar today.
Bob Wright
(Boy, do I tend to get long winded!)