The Chabad custom and possibly others is to use a chicken neck as the zero'ah.
Why specifically do we use a chicken to substitute for the Korban Pesach and not any other animal or fowl?
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Since the zeroa symbolizes the Paschal sacrifice, which was roasted, the custom is that the zeroa is roasted as well. However, since it is absolutely forbidden to sacrifice outside of the Temple Mount, and we do not want it to appear as if we are (heaven forbid) eating an actual Paschal sacrifice, we do not eat the zeroa. This is also the reason some prefer to use limb of a bird (which does not at all resemble the Passover offering, which was a lamb or a kid), and then strip much of the flesh from the bone (see: Rebbe’s Haggadah). If you follow this custom, take care that some of the flesh should remain or it is not considered a zeroa (see: Shulchan Aruch Harav 673:22, quoting the Ran).
Following this line of reasoning, this would seem to rule out using other animals for the zeroa since it could be mistaken for the Paschal sacrifice.
In terms of why a chicken, I think @DoubleAA's comment is correct: there's no kosher bird for consumption that was and is more prevalent/ accessible than a chicken.
Thus, while one could potentially suggest to use one of the aforementioned birds as their zeroa (obviously not before CYLOR) it's understandable how the widespread practice of using a chicken bone for zeroa was adopted.