Can hydrogen undergo alpha decay

No, it cannot. Fission is the "splitting" of an atom, and a hydrogen atom will not fission. Some hydrogen atoms have a neutron stuck to the proton in their nucleus. Some even have two neutrons stuck to that proton. These neutrons can be "knocked loose" in something like a nuclear chair reaction in a weapon. The neutrons then can contribute to the building of the nuclear chain reaction. But fission doesn't happen to hydrogen.