A magnetic field fails to cause deflection in

Gamma rays are high-energy electromagnetic waves and do not carry any charge.

The magnetic force on a moving particle is given by $\vec{F} = q(\vec{v} \times \vec{B})$. Since the charge $q = 0$ for gamma rays, the magnetic force acting on them is zero.

Alpha rays are positively charged, beta-minus rays are negatively charged, and beta-plus rays are positively charged, so they all experience a magnetic force and are deflected.

Therefore, a magnetic field fails to cause deflection in gamma rays.