Colt38,without seeing a photo of the piece,at the minimum,it would be difficult to give an estimate of value.
The .357 Magnum chambering in the New Service,was introduced around 1936,or a wee bit later than when the cartridge was first introduced in the S&W .357 Magnum.Some SAA's were built in .357-but damm few.
The .357 was built on the ".38 Special" version of the New Service. This model came out around 1931(along with the companion target model called the Shooting Master. They had smaller,rounded butts,and their barrel lengths were 4,5 and 6 inches,versus 4.5,5.5,and 7.5 for the other calibers. The Shooting Master was "only" in 6".
A couple of "cautions" on this .357 : 1)Colt dumped many parts on the market in the 50's,and some new .357 cylinders and bbls. were installed on older New Services. ANY serial number below somewhere in the 335,000 range did NOT start out as a .357 New Service(I can't give you the exact range,as my books are not here where I type this,from memory).2)Numrich Arms,now Gun Parts Company,made up a bunch of .357 New Service barrels/cylinders,to convert older New Services. Some of the bbls. were as long as 8". They have a ramp front sight,and of course NO Colt markings.3)I mentioned the round butt earlier,but some .357 New Services,were ordered with the square butt,and even some with lanyard rings,especially for police depts.
Keep in mind that these models were only made for 4-5 years in .357 caliber,as New Service production stopped in W.W. 2,never to resume,sadly,at the wars end. There are not many out there say as compared to .45 Colt,or the "1917s",and over 100 were sent to Britain in 1940-41,and most are stamped with the British proofs,
Hope this helps,