You specify .38, but not which cartridge. You also specified "J" Frame so that limits the time frame to post 1961. The possibilities are:

.38 Regulation Police, longest barrel 4".

.38 Special Model 36, longest barrel 3".

Yes, there are target-sighted J-Frame guns in .38 Special, a Chief's Special variant.

If you want to include .357 Magnum J-Frame guns then the options are greater. There are target-sighted Model 60 revolvers in a 3", under-lugged barrel, and the Model 60-18 which is the only J-Frame revolver other than the Model 35, a .22 cal, to have a barrel longer than 4". Another poster attached a photo of the 60-18. This is the only production I, Improved I or J-Frame S&W ever to have a barrel longer than 4 1/4" in standard production with the noted exception of the .22-.32 Target/M-35 already mentioned.