When introduced in 1956, the 44 Magnum was listed as being available with a 4 or 6 1/2-inch barrel. However, the 4-inch guns were not generally available until very late in 1956 or early in 1957. The 4-inch guns were shipped from about November 1956 until May 1957 when the 4-screw version largely replaced the 5-screw guns. We don't know how many 4-inch guns were made, but of the six thousand plus 5-screw 44 Magnums shipped, the 4-inch is seen less often by far. I wouldn't call the 4-inch guns rare or even scarce, but they are highly collectible when in 98 percent or better condition.
The 8 3/8-inch guns were first shipped in late 1958 and the special order of 5-inch guns (except for 4-5 early ones) began to be shipped in March 1958 and continued to be shipped off and on until 1963 (a few later than that) with approximatley 400 being made.
Sounds like you have a great example of an early 4-inch 44 Magnum with its original presentation case.
Bill