A GRU defector claimed that the KGB made a bunch of them and scattered them about, but I'm not sure anyone takes that super seriously. There isn't any real evidence that this happened and there are a lot of reasons to think it is unlikely.

From a technical point of view, making light-weight nuclear weapons that could be transported in very small volumes is not easy. Nuclear weapons are inherently heavy because fissile material is extremely dense, and small weapons are not efficient weapons, so you need more fissile material in it than you would need if you were making a very efficient weapon but were unconstrained by size.

The lightest nuke the US ever made was the W54, which at about 50 lbs was man-portable (though might be hard to manage with one hand and not be obvious about its weight) but not something you'd throw in a suitcase (it was transported in a backpack), and not the right dimensions to fit into a suitcase (it was relatively bulky). It could probably fit in a duffle bag, though.

To my knowledge the US never made weapons that would fit into a suitcase — suitcase bombs had no place in US nuclear doctrine (if they wanted a small nuke somewhere, they would either drop it from a plane, shoot it on a missile, or parachute a guy in with it strapped to his back).

Even if you wanted to smuggle a nuclear weapon in a diplomatic pouch, you would not need to make it a suitcase bomb, because presumably you could bring it in separate pieces (each of which could easily be man-portable and small enough to fit into a suitcase) and assemble it at the destination.

Note that weapons of these small sizes, like the W54, are very low yield by nuclear standards (1 kiloton or less). This is related to the efficiency problem I mentioned earlier. Small sizes and weights constrain your ability to build efficient tampers, neutron reflectors, and high-efficiency detonation systems.

I cannot comment on any supposed briefcase nuclear weapons, but the United States did develop a "backpack" nuke during the 1950s and 1960s.

The SADM (Special Atomic Demolition Munition) was a small nuclear weapon that could be carried by one man, in a large case that would be carried on the back of a trooper or Special Forces Operative. This video shows how it would be operated. https://www.youtube.com/watch?v=n4NZmPlAGBQ

The weapons themselves were, again, not exactly suit case size. The smallest known weapon in the American Nuclear arsenal was the W54, which weighed at least 50 pounds and had a yield ranging from 10-1000 tons, depending on the configuration. (For perspective, that's about 0.06%-6% the yield of the Little Boy bomb dropped on Hiroshima). Much tinier (although a few tests did reach higher yields of a few kilotons).

The W-54 was also used for the Davy Crockett, which was essentially a very large recoilless rifle with a nuclear payload. They were deployed in Europe for about ten years, with US Army Forces.

If you would like some sources, I would be happy to go grab my books back from my room in a few hours.