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.
Answer
I think this would be tricky, since any force mediator (at least from conventional thinking) must have a three-valent vertex, two of which are the charged object and one of them is the force carrier. If the force carrier is a fermion, I don't think this combination can be Lorentz invariant (spin zero combination).
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