I agree it is likely the "E" from the word "DIME" on the bottom of the reverse of a Roosevelt dime. It would make sense as a dime is much thinner and easier to cut up with the right tools. The creator removed part of the nickel to drop the fragment into the divot he created to try and match the thickness. The top and right side are also too smooth and straight to be a scrap piece struck on a nickel, even if everything else matched up. Lastly, notice how even and smooth the top and right parts of the fragment are, and how the left side and bottom are rough and uneven. This is because there was an "M" before the "E", which was harder for it to be cut nice and flush since the "M" is raised. There is no letter to the right of the E in DIME, and there is a lot of open space above it, making it easier to cut nice and straight/even. And the bottom is rough because right below it, you have the rim/edge of the dime showing the reed pattern, which the creator of this piece likely wanted to hide.
I'd agree with the above post - notice that the "E" piece is both lighter, and a sharper strike than the circulation on the host coin. It's not part of a minting process error, imo. Added afterward; not sure exactly how, but it doesn't fit the coin