The three-cent bronze was a pattern coin struck in 1863 by George Eckfeldt.
[1] The coin shares its obverse design (other than the font of the date, which is smaller and curved), thickness, and diameter with that of the Braided Hair large cent, but was made of bronze rather than pure copper.
Throughout 1863, the coins were struck on planchets of varying thickness.
According to Eckfeldt's journal: Struck a few 3 cent pieces of copper & zinc; the size, thickness and diameter about that of the 1857 copper cent.
[1]An aluminum version (Judd-320, Pollock-385) was made using a very similar design.