First off, it's not a Schofield as they weren't made in that chambering. (Unless it's a conversion.)
There are only three S&W top-break models chambered in 38/40. They are the New Model #3, the New Model #3 .38 Winchester (same as the former but in their own serial range). Both of these are single action. Then there is the .38 Winchester Double Action. Regardless of which one of these it turns out to be, they are all a rare/scarce gun.
If it is a "regular" NM#3, it probably was a special order. If a NM#3 .38 Winchester, it is 1 of 74. (very scarce!)
Finally, if it's the double action, it is 1 of around 2000. (Still scarce). Any one of these is very desirable. You will definitely need to get a factory history letter to authenticate what you have.
Nice inheritance!!