A "ticket" is an arrest where they don't take you into custody. They release you to appear in court later to either plead guilty or demand a trial and fight the charge. All tickets offer the opportunity to plead guilty by mail (or drop box, etc.), and they state clearly on the ticket that paying the fine constitutes entering a plea of guilty (or "no contest," which allows the judge to find you guilty because you are not fighting the charge).
If you did not have it deferred (which you might have, because you would then have paid a "fee" instead of a "fine"), then it should appear on your record, if all the records have been properly kept, which does not always happen.
You may get by with saying that you thought it was dismissed, because that often happens. All employers, including law enforcement agencies, set their own policies -- e.g., "no tolerance," "no weight given to Class C infractions," "consider only incidents that happened before the applicant was 18 YOA," or "that are less than 20 years old," etc.
It is unlikely that you can get it removed now, but maybe not impossible. Might be worth looking into.
This answer is intended to be taken as general information and not as specific legal advice. You should always consult a qualified attorney and make him familiar with all the relevant facts in order to get proper legal advice. Every case is different, and they must be evaluated on a case-by-case basis. David N. Smith 812 W. 11th Street, Suite 201 Austin TX 78701 (512) 457-0100 defenseattorneysmith.com
Mr. Smith is correct. One place I always start is to check with the court. Whether it's a municipal court of a county justice of the peace court, the clerk's should have records and be able to pull your file up by name, date of birth, driver license number, and year of the offense. Make sure you go to the correct court. Another option is to pay to run your criminal background through a private service like publicdata.com. Good luck to you.
If you paid off the ticket, and received no paperwork from the court outlining some sort of Deferral Requirements, this charge most likely resulted in a conviction on your record. If you want to make sure, I would suggest paying for a background check from a private online service, or going to the Texas DPS website to see about getting a background check.
There is no way to know how the LE job will look at this conviction, unless you go straight to the source, and ask them how much they weigh class C convictions. Remember that drug and alcohol related offenses are often handled differently than a mere speeding ticket.