There are two different concepts for so-called "enhanced radiation" weapons. The first is the well-known but oft-misunderstood neutron bomb. A neutron bomb is simply a small nuclear weapon (< 1 kt) that uses radiation as its primary destructive method. There isn't anything special about a neutron bomb, except that its explosive yield is small enough that its radiation lethal range happens to be larger then its blast radius. It was to be used against enemy tank formations, since tanks are well protected from the blast effects of nuclear weapons and you don't want fallout coming back over your own troops. A neutron bomb would create lethal radiation to enemy tank crews that could be used relatively close to friendly forces.
The other ER weapon is called a salted bomb. The way fusion bombs work is they use a fission bomb to create the heat and pressure necessary to create fusion in a secondary chamber. The fusion reactions that take place create lots of extra neutrons, and these neutrons cause additional fissions in a uranium layer on the outside of the bomb to increase the explosive power even further. However, if you wanted to make an insidious weapon that would case long-lived deadly fallout, which would render a large area inhospitable for years, you could replace the outer uranium layer with cobalt metal. When natural cobalt-59 absorbs neutrons, it becomes cobolt-60, an isotope which emits a strong gamma ray with a half life of 5 years. If you detonated such a weapon at high altitude over a populated area, the blast may not damage structures but the fallout would require the population to take shelter or evacuate for an extended period of time or perish to radiation poisoning.