You'll have to use aws s3 sync s3://yourbucket/
There are two parameters you can give to aws s3 sync; --exclude and --include, both of which can take the "*" wildcard.
First we'll have to --exclude "*" to exclude all of the files, and then we'll --include "backup.2017-01-01*" to include all the files we want with the specific prefix. Obviously you can change the include around so you could also do something like --include "*-01-01*".
That's it, here's the full command:
aws s3 sync s3://yourbucket/ . --exclude "*" --include "backup.2017-01-01*"
Also, remember to use --dryrun to test your command and avoid downloading all files in the bucket.