First the plus. The coin is well struck. A fully struck "III" is not rare but not common either.
My source (Flynn's book) doesn't show a variety with a Cud; you need to find another reference. I can't tell if it's an RPM since there's too much crud in the date. And the black "toning" on the obverse is a real downer (stored poorly?)
It looks like a rim Cud to me, but I agree the coin does look like it has been plated as well, long ago. Contemporary to try and pass as a dime? The dime and the Three Cent piece were both the same size 17.9 mm.
Interestingly, here's another 1888 cn Three Cent piece with a Cud .... same seller, same price. I prefer this one, clashes and all, as the other example has the appearance of being plated.
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