We consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis and then returns to the initial point closing the orbit. When the parameters of the family are restricted to certain explicitly computable open semi-algebraic sets , we characterize those parameters that give rise to the appearance of local two-dimensional periodic invariant manifolds through the singularity. Also we use a Bautin-type analysis to study the maximum number of small-amplitude ν-limit cycles that can be made to bifurcate from the equilibrium when the parameters of the family are restricted to . We obtain global upper bounds on the number of bifurcated ν-limit cycles.