I'm not sure if you are joking or for real. Cents weight between 2.5 and 3.11 grams depending on the year.
A quarter that was struck on a nickle planchet - no wait, a cent planchet but doesn't have the right weight and found in a roll of buffaloes -
The eagle on the reverse wouldn't fit on a cent so you can rule that out. Agreed that it is just a damaged quarter.
You THINK it's PMD? OH yes let's run a coil of quarter strip through the nickel blanking press, and then take the nickel sized clad planchets over to the quarter press. Let's see three different major unlikely errors, or PMD Hmmm.
The current clad version is two layers of cupronickel, 75% copper and 25% nickel, on a core of pure copper Here is an example of a Quarter missing clad top layer from my collection -