We consider the motion of an infinitesimal mass under the Newtonian attraction of N point masses forming a ring plus a central body where a Manev potential (- 1 / r+ e/ r2, e∈ R), is applied to the central body. More precisely, the bodies are arranged in a planar ring configuration. This configuration consists of N- 1 primaries of equal mass m located at the vertices of a regular polygon that is rotating on its own plane about its center of mass with a constant angular velocity ω. Another primary of mass m= βm (β> 0 parameter) is placed at the center of the ring. Moreover, we assume that the central body may be an ellipsoid, or a radiation source, which introduces a new parameter e. The existence and stability of periodic solutions of the spatial Maxwell restricted N+ 1 -body problem is obtained using averaging theory. The determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. The planar case is moreover considered.