We employ a high-dimensional version of the Marcinkiewicz exponent, a metric characteristic associated with non-rectifiable plane curves, to directly address the resolution of certain Riemann boundary value problems on fractal domains within the Euclidean space \(\mathbb {R}^{n+1}\) , were \(n\ge 2\) for Clifford algebra-valued monogenic and polymonogenic 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 nature of this theoretical result, we characterize a class of hypersurfaces where our results offer a greater level of refinement compared to those previously reported in the literature.