You can use a scanning/trimming program like bbduk.sh in filter mode (guide: https://jgi.doe.gov/data-and-tools/software-tools/bbtools/bb-tools-user-guide/bbduk-guide/ ) to see if those sequences are present in your data.

Another way would be to use the bloom filter in BBMap suite to quickly identify reads that share k-mers with your sequence of interest.

All GenoMax said. Or you can align your reads to a reference genome that only contains your plasmid sequence