The focal plane spot size of an optical lens is limited by its numerical aperture (NA) and wavelength of input light beam and therefore, input beam cannot be focused beyond the diffraction limit λ/(2NA) also known as Abbe limit. However, by modulating the input beam with an appropriate mask much smaller focal spot is obtained, accompanied by additional rings of light. This is a manifestation of a super oscillating function – a band limited function that oscillates locally faster than its higher Fourier component. Here we present a systematic method for structuring the sub-diffraction lobes of super-oscillating (SO) beams. We both numerically and experimentally show that how the amplitude and phase profiles of Gaussian, Hermite-Gauss, Laguerre-Gauss and Airy functions can be used to modulate super-oscillating (SO) optical beams with lobe size beyond the standard diffraction limit. Further, for the first time these structured SO beams are used for high resolution trapping and manipulation of nanometer-sized particles. The trapping potential provides unprecedented localization accuracy and stiffness, significantly exceeding those provided by standard diffraction limited beams. Despite the lower power of the SO beam, the trapping stiffness is observed 44 times higher than that achieved by diffraction limited Gaussian beam. The sub-diffraction spots of the structured beams may be applied for STED microscopy and in lithography. Further, this method can be used in other fields, e.g. nonlinear frequency conversion, plasmonics, structuring light pulses in time domain and for time-dependent focusing.