If you successfully completed a DADJ then the judge would have entered an order dismissing your case. Therefore you were never convicted of the charge as far as general Texas law. You would have to answer "yes" if asked whether you were arrested, but you can answer "no" if asked if you were convicted.
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You are asking two different questions. First, how you answer the question on the job application depends on what the question is. If you are asked if you've ever been convicted of a felony, you can say no. If you are asked if you have ever been charged, you must say yes.
The case has already been disposed of, so you cannot turn it into a dismissal at this point. However, a deferred is sort of like a dismissal. You just can't expunge it from your record like an outright dismissal. HOWEVER, you can seal the record so that only the government can see it. After the record is sealed, you can answer no the question "Have you ever been charged with a felony?" because the employer doesn't have the right to know about it.
Call a few attorney who practice in the county where the case was filed. They can walk you through the process.
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Presumably, your case already has been dismissed, unless you got into trouble and ended up getting adjudicated for the offense. But it will remain on your record unless and until you get what's called an order of nondisclosure. If your case is that old and you've stayed out of trouble other than that one time, your chances are probably pretty good. It has to be handled as a separately filed case, and it takes several months gor the effects of the order to actually be seen on a background check. If this was in Harris County, their judges require you to attend a brief hearing where the judge willl listen to why you want the nondisclsure, plus any input from the prosecutor as to the circumstances of the offense, reasons you should or shouldn't get the records nondisclosed, and will then make a decision based on all that. Given that it's completely within the judge's power to grant or deny these, your odds really are better if you hire an attorney who's familiar with them. Good luck.