It is used very rarely. It is old-fashioned and flowery. It is most often used in the phrase "of paramount importance." Usually you can just use a plain word like "most" or "highest" and usually it is better to do so.
"To a journalist, accuracy is of paramount importance."
"The paramount question of the age is how to deal with climate change."
"The politician said that a border wall would benefit both nations, because safety is the paramount concern of both."
Here's an example of the style of writing that uses words like "paramount:"
"Not for two centuries, since the historic strife of Anglican and Puritan, had our island produced a ruler in whom the religious motive was paramount in the like degree."
P.S. I could give a flippant but accurate answer and say that in the United States, _by far_ the most common use of the word "paramount" is when mentioning the movie company, Paramount Pictures Corporation. Thus, the most typical usage would be something like:
"Paramount has canceled the movie, 'Mission Impossible: 6.'"