Looking at the comments of this questions Does the gravitino contribute to the gravitational interaction? and even considering that the answers here in this other question Why are all force particles bosons? do explain why a force carrier needs to be bosonic, I still wonder if there are some particular cases where a fermion similar to a gaugino could mediate a force.
A case in mind, that could avoid the issues on angular momentum conservation, is zero-range interactions ("contact" interactions). Still, I can not see how such beast could be described with a Lorentz invariant Lagrangian.