Certainly there were some. There was a well-known novel by Yulian Semyonov called "17 Moments of Spring", about a Soviet spy - that is, an intelligence operative - in Berlin during WW2. The movie series based on the novels, also called "17 Moments of Spring", was popular to the point that the streets were noticeably empty when it was on television, and both the series and the various characters from it remain iconic in Russian culture to this day. Stierlitz, the spy hero of the series, is the person who everyone would name as the Soviet equivalent of James Bond, in the sense that he was a superspy. But he is not really a similar character.

There were several other movies and novels with intelligence and spying themes, e.g. "The Shield and the Sword" and "In the August of 44", almost always in a WW2 setting. "In the August of 44" had many consultants from the security services and is supposed to be an accurate representation of counterintelligence work.

If you mean specifically Cold War spying and intrigue, then the same Semyonov also wrote "TASS Is Authorized to Declare...", which was also turned into a film series. It was well-known at the time, but did not leave as deep a cultural imprint as "17 Moments".

But in general, the USSR had very few films or novels even set in the contemporary Western world, and very few fictional treatments of Cold War confrontations. One exception is the movie "The Detached Mission" or "Solo Voyage", which had American bad guys, and which I remember hearing at the time being called "retaliation" for various American movies with Soviet villains. However, there were too few American characters of any sort in Soviet literature or film to make much of an impact, and the USSR "retaliated" very little in this way, despite complaining bitterly about their own representation in Western movies - I recall a lot of noise about one of the Rocky movies in which a Soviet boxer kills an American in the ring.