Yes,it is an 03A3 semi-pistol grip. Altered from designs for a full pistol grip that was adoptéd during the 30's,for wartime ease of manufacture. Many hate their looks, but they tame that 03 recoil very well, indeed. They can be used on all the Springfield variants.
Your stock is what was called the "scant" stock and was an alternative to the C stock that could still be cut from the "S" (straight) stock blank, because they had too many S blanks still in inventory. Anyhow, yours appeared to have been made during WWII and should be able to fit both the 1903 and 1903A3. Post some close-ups and I will tell you which manufacturer made it.
If it is a Springfield there will be a small "s" in the cutoff notch (left side). There were several manufacturers of them. Springfield, Keystone (upside down "K" in the cutoff), American Bowling and Billiard, Milton Bradley and The Embossing Company.
Prior to WWII Springfield was the only manufacturer and they fit only the 1903. That changed when the war broke out and all Springfield C and Scant stocks went to the 1903A4 program, also prompting the minor mod for use on the 1903A3/A4. That's when the other manufacturers were brought on and started production.
I'll send you a message, I'd be interested depending on condition.
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