There are a few ways that magnetic fields and proton beams interact:
Proton spin
Protons have a magnetic moment due to a quantum property called spin, which makes them act like tiny bar magnets. When placed in an external magnetic field, a proton's spin can either align with the field or flip to oppose it.
Proton movement in a magnetic field
When a proton moves in a magnetic field, it experiences a force that causes it to move in circles. The magnetic field "steers" the charged particle, but it doesn't make it speed up or slow down.
Proton beam and magnetic field direction
If a proton beam moves parallel to a magnetic field, no force acts on it, and it continues moving in a straight line.