California and Ohio are both members of the Drivers License Compact so the Ohio court system or OH Bureau of Motor Vehicles will send information to the CA DMV about this ticket if you plead guilty and are convicted of the speeding violation.
In Ohio, going 11 to 29 mph over the posted speed is a 2 point offense. According to the California violation points assessment list out of state violations, speed/too fast or over the speed limit offenses are assigned 1 point. So most likely the out of state speeding violation would go on your driving record and be assessed one point.
You can check with the California DMV to see if you can take traffic school but it is doubtful that it would help take this ticket off of your record since the offense occurred out of state. You might see if Ohio will allow you to take a defensive driving course or traffic school to dismiss the ticket and thus not report it to back to your home state.
If you end up with the speeding ticket going on your CA driving record it could affect your insurance premiums depending on how your insurance company rates this type of moving violation. Read our article What a Traffic Ticket Can Truly Cost You for more information on this topic.
You can still look for budget car insurance at CarInsurance.com.