  We investigate the regularity of the solutions for a class of
degenerate/singular fully nonlinear nonlocal equations. In the degenerate
scenario, we establish that there exists at least one viscosity solution of
class $C_{loc}^{1, \alpha}$, for some constant $\alpha \in (0, 1)$. In
addition, under suitable conditions on $\sigma$, we prove regularity estimates
in H\"older spaces for any viscosity solution. We also examine the singular
setting and prove H\"older regularity estimates for the gradient of the
solutions.
