Using the find command
Delete all 0 length files
find /path/to/directory -type f -size 0 -delete
or
find /path/to/directory -maxdepth 1 -type f -size 0 -delete
Delete all 0 length files
find /path/to/directory -type f -size 0 -delete
or
find /path/to/directory -maxdepth 1 -type f -size 0 -delete