It used to be, if you got a ticket in another state that wasn't in NY's computer system, if you paid it in the appropriate timeframe, it wouldn't go on your license (only NY, NJ, FL, CT all talked to each other in the 80's/90's), but not so anymore.
That and you are still in NY State even if you are in Western NY which can be up to 450 miles away.
The best that you can do, is pay $100 and take a 9 hour defensive driver course and knock some of the points off of your license.
Otherwise, your 4 points will fall off in 18 months. If you get 2 more points (for a total of 6) they tack on a $300 surcharge onto your already existing pain, and if you get another ticket, they will suspend your license for 90 days, except for work or school.
A lawyer won't help if they used a handheld radar detector. They got pics of you in the act and have to state that the radar was calibrated B4 nailing you, so lawyers can't beat the ticket like they used to be able to do.