Popcorn, your revolver uses .32-20 ammunition. It's a little difficult to find (and expensive), but it is still loaded and out there if you look for it. And it is safe to use in your revolver. Everyone seems to always want to jump in with a dire warning about how dangerous it is to fire the high-velocity rifle round in a revolver, but that is untrue. First, back in the day, it was done all the time, and revolvers did not blow up. Second, that HV rifle ammo has not been manufactured in over 50 years, and you are not likely to find any. All .32-20 ammo of current manufacture is perfectly safe to use in .32-20 revolvers, including yours. Those revolvers with the barrel stamped as .32 Winchester are early ones, 1914 and earlier. The .32-20 K-frame revolvers were serial numbered separately from those in .38 Special, and there were only about 144,000 of them made from 1899 until the late 1920s, as compared to millions made in .38 Special, so they are a bit unusual.
Your revolver is not an antique, and further questions should be posted in the hand ejector portion of the forum.