Is there some special case where a fermion can mediate a force? 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.
 A: It depends  on your definition of force. Force means a change in momentum, ~dp/dt  , so any change in momentum in a Feynman diagram is a force. For example this diagram for compton scattering 

says yes.
If one is talking of gauge theories and exchanged bosons , because those are the ones that build up the  three, electromagnetic, weak, strong ( maybe four if gravity is unified) forces , then no, by the construction.
A: 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).
A: It depends what you would accept as a valid answer but two bosons could feel a small force resulting from a virtual fermion loop for example. Does that count?
A: Besides the need of having a Lorentz invariant term, there is another "against" that comes only when we consider classic fields. If we restore units, a Planck constant appears in the kinetic term of the fermion field, telling that it will disappear in the limit $\hbar \to 0$. But of course this "non-go" argument is bypassed by any macroscopic electrical current. 
