We investigate types of turbulence generated during particle acceleration in 3D Harris-type reconnecting current sheets (RCSs) with magnetic islands, using the particle-in-cell approach. When a guiding magnetic field is present in the RCS, protons and electrons become separated at ejection into the opposite semi-planes, or footpoints of reconnecting magnetic loops, due to the opposite gyration. The particles of the same charge (ions or electrons) ejected from the RCS from the opposite side where they enter called ‘transit’ particles. They are strongly energized and form unidirectional beams in the pitch-angle distribution. While the particles that move back to the same side where they enter the RCS are called ‘bounced’ particles. They gain less energy and form more diffusive pitch-angle distributions. In the RCS with magnetic islands, these two groups of particles are ejected from the X-nullpoint at the end of the islands forming the similar asymmetric distributions in the opposite separatrices. The energy difference between ‘transit’ and ‘bounced’ particles forms ‘bump-on-tail’ velocity distributions that naturally generate plasma turbulence. Lower-hybrid waves are generated into the magnetic islands, owing to the two-stream instabilities. The presence of the anisotropic temperature inside the RCS can introduce whistler waves. High-frequency fluctuations, upper hybrid waves or electron Bernstein waves, pile up near X-nullpoints, which are consistent with MMS observations. We present the wavelet analysis and energy spectra of the turbulent electric and magnetic field fluctuations for different frequencies. The results can be beneficial for understanding in-situ observations of energetic particles in the heliosphere with modern space missions.