You are correct New York and California share information regarding traffic citation their licensed drivers receive under terms of the Drivers License Compact. They do not however share the same points system.

In New York for example a conviction of a speeding ticket for 11 to 20 mph over the posted limit is a 4 point offense. While in California speeding is a 1 point offense whether the speeding violation occurred in or out of state.

You will need to check with the courts in New York where you received the speeding ticket to find out if there is a way in which to take traffic school so that this ticket is not recorded in New York or California. It may be possible that if you take a driving course through NY that the ticket is dismissed or not seen as a conviction and thus not transferred to California.

If instead the ticket information is reported to California it will likely be placed on your CA driving record and assigned points. It is doubtful that you could take traffic school in California to erase the ticket or points.

In CA to take traffic school you must be approved by the court clerk or a judicial officer in the county in which the citation was written. Since the ticket was not received in California this does not seem possible but you may check with the CA Department of Motor Vehicles to make certain.