There is an effect called Landau quantization which quantizes the cyclotron orbits (and thus energy levels) of free charge carriers in magnetic fields. For ordinary physical conditions (magnetic field strength, room temperature), the effect of a magnetic field on the energy band gap of a typical semiconductor is probably negligible. This energy quantization leads to the de Haas-van Alphen and Shubnikov-de Haas effect which can be observed at very low temperatures and large magnetic fields. The latter appears at very low temperatures in semiconductor inversion layers found in field-effect transistors. Such a quantized inversion layer is also called a two-dimensional electron gas.
You will probably not see any effect due to a change in energy band structure by putting a semiconductor diode into a a magnetic field. A much stronger, but still small effect would be the magnetoresistance. The "threshold voltage" of a semiconductor diode is a poorly defined technical, unphysical concept. It will probably not show a visible change.