What is the name of the agreement between the USA and the USSR that limited
nuclear weapons? *

The Nuclear Test Ban Treaty.

Explanation: This treaty was signed in 1963, as representatives of the United States, Soviet Union and Great Britain signed the Limited Nuclear Test Ban Treaty, which prohibited the testing of nuclear weapons in outer space, underwater or in the atmosphere.

which time period is this? or is this story fictional, i'm going to need more info to answer this question

this isn't a question and if you're going to list things be kind and use commas.