Am I right?
No you are not correct. The crontab manual states:
Note: The day of a command's execution can be specified in the following two fields day of month, and day of week. If both fields are restricted (i.e., do not contain the "*" character), the command will be run when either field matches the current time. For example,
30 4 1,15 * 5
would cause a command to be run at 4:30 am on the 1st and 15th of each month, plus every Friday.
So how can we do it?
If you want to determine which Saturday of the month it is, i.e. whether it is the 1st, 2nd or 3rd Saturday of the month, all you have to do is look at the weekday of the Saturday and do the following integer computation:
D=$(date "+%d")
echo $(( (D-1)/7 + 1 ))
This value will return the corresponding number. This does not only work for Saturdays but for any Weekday.
Since the OP wants the cron to work on the 1st, 3rd and potentially the 5th Saturday, it actually states that the cron runs on every odd-numbered Saturday:
D=$(date "+%d")
echo $(( ((D-1)/7 + 1) % 2 ))
Using this as an additional test, allows us to write the cron as:
# Example of job definition:
# .---------------- minute (0 - 59)
# | .------------- hour (0 - 23)
# | | .---------- day of month (1 - 31)
# | | | .------- month (1 - 12) OR jan,feb,mar,apr ...
# | | | | .---- day of week (0 - 6) (Sunday=0 or 7)
# | | | | |
# * * * * * command to be executed
30 16 * * 6 (( (($(date "+\%d") - 1)/7 + 1) % 2 == 1 )) && command