Light is an example of this.  Light appears in some respects as a continuous electromagnetic wave, on the submicroscopic level is emitted and absorbed in discrete amounts, or quanta; for light of any given wavelength, the magnitude of all the quanta emitted or absorved is the same in both energy and momentum.  These particlelike packets of light are called phtons, a term which is also applicable to quanta of other forms of electromagnetic energy such as X rays and gamma rays.  Submicroscopic mechanical vibrations in the layers of atoms comprising crystals also give up or take on energy and momentum in quanta called phonons.