When was the hydrogen bomb dropped?

I don't know about the USSR. The first US drop was on 20 May 1956, on Bikini Atoll in the Pacific. The bomb was dropped from a B-52 at 50,000 feet, and exploded at 4,330 feet. The yield was 3.8 mega-tons.

Following is about fusion bomb tests, not about bombs dropped.

The "George" shot of Operation Greenhouse of 9 May 1951 tested the basic concept (of a thermonuclear fusion bomb ignited by a smaller fission bomb ) for the first time on a very small scale. As the first successful (uncontrolled) release of nuclear fusion energy, which made up a small fraction of the 225 kt total yield, it raised expectations to a near certainty that the concept would work.

On November 1, 1952, the Teller–Ulam configuration was tested at full scale in the "Ivy Mike" shot at an island in the Enewetak Atoll, with a yield of 10.4 megatons (over 450 times more powerful than the bomb dropped on Nagasaki during World War II).

The Hiroshima and Nagasaki bombs were both fission (atomic) bombs, not fusion (hydrogen) bombs.

Several bombs have been dropped for test purposes and a few have been dropped accidentally (but did not explode!).

on Nagasaki in 1945 killing a 100,000 humans in and instance and thousands more from the fallout later for years later

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