Actually, they only made the 1 tiyin coin in one year, 1994. Virtually no Uzbek coins have been issued for more than one year; like most other post-Soviet states, they have had serious inflation problems since independence. The Uzbek government is officially in denial about the inflation the country has had since then, which is why they've never formally withdrawn the "worthless" denominations. Coins no longer circulate at all in day-to-day use in Uzbekistan. The largest face value note in the country, the 5000 som (which was only released in July 2013), has an exchange value of US$2.36.
The "world's most worthless coin" tag seems to derive from
this BBC news article back in February. It's also the derivation of the "1 tiyin = 1/2000th of a cent" figure. The inflation in Uzbekistan has, of course, gotten worse since February. 1 tiyin is now worth 1/2115th of a US cent.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis