Alpha particles are positively charged, beta particles are negatively charged, and gamma radiation is electrically neutral. This means that alpha and beta radiation can be deflected by electric fields, but gamma radiation cannot.
Remember that opposite charges attract. Beta particles are negatively charged so they will be attracted towards a positively charged plate. And positive alpha particles will be attracted towards a negatively charged plate.
Because they consist of charged particles, alpha and beta radiation can also be deflected by magnetic fields. Just as with electric fields, gamma radiation is not deflected by magnetic fields.