Hi,
According to the Smith & Wesson book by Jim Supica & Richard Nahas the M13 evolved from the M10-6. The 10-6 was a prototype of the later model 13 chambered in 357. FBI issued the model 13 in 1974 and 1986 to 1987. The 13-1 was introduced for the N.Y.S.P in 1974. I have a model 13-2 4 inch made in the 1977 era. One of my favorite K frame magnums.
Howard