The 1903A4 was the sniper model with factory installed scope sight and no iron sights. They are still marked Model 03A3 but with the serial number and model designations offset to be visible beside the front scope base. It is a top mount, not a side mount like 32 Magnum thinks it has.
If you have one of those and it has not been messed with other than changing the scope and stock and if you can get the original stock for it, and if you can find an original scope mount and if you don't mind paying for an original or at least period scope, it will be a nice and valuable rifle.
Don't get all tangled up in the two groove barrel business. They were just as accurate as four (or six) groove barrels with military ammunition in military rifles.