In two recent papers, it has been demonstrated that, beside usual scattering and optical forces, new optical forces and terms are exhibited when a Rayleigh particle is illuminated by an off-axis Bessel beam. Namely, (i) axicon optical forces are associated with scattering optical forces and (ii) additional axicon terms are associated with gradient optical forces. These extra-axicon forces and terms are zero when the axicon angle is zero and/or (most often) when an on-axis configuration is considered rather than an off-axis configuration. This study was devoted to longitudinal forces. The present paper is devoted to transverse forces and demonstrates the existence of newly additional axicon forces associated to both the usual scattering and gradient forces. Again, these new extra-axicon forces are zero when the axicon angle is zero and/or when an on-axis configuration is considered rather than an off-axis configuration.