When I worked for Ruger in the 1980s fixed sight revolvers for government contract orders were commonly zeroed using the specified ammunition provided as government furnished material. While the specs varied in accordance with the contract specifics most .38 Special or .357 revolvers would commonly be shot off sandbags at 20 yards, aiming at a 2-inch bull, or if at other ranges the aiming point was scaled to one inch per ten yards.
At the 20 yard distance most often used, a 3" circle was printed on the target, surrounding the 2-inch aiming point and tangent to it at 6:00. Five out of six rounds were usually required to strike within the 3" circle. The correct front sight height would be determined by firing a ten-board sample of revolvers with the contract ammunition to obtain the correct elevation, that sight then being installed on all revolvers for that batch. Windage adjustments were made, when necessary by rotating the barrel in the frame using directed strikes with a babbit bar against the ejector rod shroud forged onto the barrel.
In revolvers point of impact for elevation is determined more by bullet weight than velocity. In .38 Special either standard pressure or +P loads of the same bullet weight generally shoot close to the same point of aim. As a general rule heavy bullets shoot higher, lighter bullets shoot lower. In ordinary production intended for civilian retail sales it was common to use .38 Special 148-grain wadcutter ammunition in .357s also because this provides a useful point of impact for most commonly used ammunition. Lead wadcutters also provide a better functional check to detect "spitters" in which a new fit-up might over-rotate the cylinder (Up to about 5 degrees being intended and OK to compensate for in-service wear).
To determine how much to adjust the fixed sights use the formula X=RE/D where:
X is the amount of correction needed, such as shortening the front sight to move the impact up, or installing a higher front sight to lower point of impact, or rotating the barrel tighter in the frame, moving the front sight left to move impact to the right, etc.
R is the sight Radius in inches.
E is the error correction needed between point of aim and point of impact, and
D is the target distance.
Again ALL dimensions are in inches.
For a gun which shoots low a heavier bullet or light dressing of the front sight will normally fix things. If the gun shoots high try a lighter bullet. In the worst case you need to fit a taller front sight.
If a windage adjustment is needed scribe a light witness mark on the frame to aid observation and then turn the barrel to tighten or loosen very slightly to bring impact into alignment. At the factory this is normally done with calibrated strikes using a lead hammer or babbit bar against the barrel ejector shroud. In extreme cases an old cop gun may have a bent frame from being used as an impact weapon, and/or the crane may be bent out of alignment. A competent gunsmith can fix these but extreme cases will require removing the barrel, refacing the straightened frame and re-installling the barrel. In light alloy frame airweight guns special fiixtures are needed to gently turn the barrel without frame damage. NOT a job for the hobbyist.
But in most cases there is absolutely no reason why a 2-inch .38 snubby cannot be zeroed precisely and shoot accurately. My S&W Model 36 former basket case reworked by Sandy Garrett of NoVa Gun Works now shoots ten-ring, 25-yard groups with wadcutters, and quality defense or service loads should do likewise in a mechanically correct gun.