  We propose a counterpart of the classical Rollnik-class of potentials for
fractional and massive relativistic Laplacians, and describe this space in
terms of appropriate Riesz potentials. These definitions rely on precise
resolvent estimates. We show that Coulomb-type potentials are elements of
fractional Rollnik-class up to but not including the critical singularity of
the Hardy potential. For the operators with fractional exponent $\alpha = 1$
there exists no fractional Rollnik potential, however, in low dimensions we
make sense of these classes as limiting cases by using $\Gamma$-convergence. In
a second part of the paper we derive detailed results on the self-adjointness
and spectral properties of relativistic Schr\"odinger operators obtained under
perturbations by fractional Rollnik potentials. We also define an extended
fractional Rollnik-class which is the maximal space for the Hilbert-Schmidt
property of the related Birman-Schwinger operators.
