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In Texas, whether a felony can be removed from your record depends completely on how the charge was resolved. If you plead guilty or were convicted by a judge(court)/jury, then there is nothing that can be done.
If you were found not guilty, the charges no-billed, or the charges were dismissed then you can likely move to have the charge expunged. If on the other hand, you successfully completed a deferred adjudication probation (not straight probation) and a sufficient period of time has passed (typically five years) then you can file a motion for non-disclosure to seal your record from just about everyone but law enforcement. If it is an eligible felony, then you must have served out the deferred and been off it for at least 5 years. The petition is filed in the court in which the case was prosecuted. The judge must find that it is in the best interest of you and the community to grant the petition. If granted, the record is sealed against many prying eyes such as local record checks.
Straight probation will not let you do this, but only deferred will. Also, certain crimes are ineligible for sealing.
You should consult with a criminal defense attorney about your options, and whether the felony is eligible. Attorney’s usually charge a fee for such a motion to seal or expunge of about $1,000-$1,500. I hope this helps.