  We investigate the cubic interactions of a massless higher-spin fermion with
gravity in flat space and present covariant 2-s-s vertices, compatible with the
gauge symmetries of the system, preserving parity. This explicit construction
relies on the BRST deformation scheme that assumes locality and Poincare
invariance. Consistent nontrivial cubic deformations exclude minimal
gravitational coupling and may appear only with a number of derivatives
constrained in a given range. Derived in an independent manner, our results do
agree with those obtained from the light-cone formulation or inspired by string
theory. We also show that none of the Abelian vertices deform the gauge
transformations, while all the non-Abelian ones are obstructed in a local
theory beyond the cubic order.
