We employ a high-dimensional version of the Marcinkiewicz exponent -- a metric characteristic associated with non-rectifiable plane curves -- to address the resolution of certain Riemann boundary value problems on fractal domains in the Euclidean space ℝᵐ for Clifford algebra-valued monogenic, polymonogenic, and inframonogenic functions, with boundary data in classes of higher-order Lipschitz functions. We establish sufficient conditions ensuring the existence of solutions to these problems. To highlight the scope of this theoretical result, we also characterize a class of hypersurfaces for which our results provide a higher level of refinement compared with those previously reported in the literature.