If your conviction occurred over three years ago you are definitely too late to appeal and the opportunity for some other post-conviction remedies has probably also lapsed.
No judge should have accepted a plea of guilty to a DUI 3rd felony without proof that two qualified prior convictions occurred. One issue of note is that if you have two DUI convictions, even if both are termed a "1st offense," a third conviction can still be a felony conviction. It is the number of DUI convictions within the statutory time period, not the nature, that counts.
You might want to find an attorney in your area who specializes in post-conviction relief. Make sure you have a frank discussion about the merits of your case and the likelihood of success before you hire anyone, though.
I completely agree with Mr. Cornick. In addition, I would like to add that there are ancient writs that are recognized in Virginia that may be available to you in your case. Additionally, you could ask for a pardon, but these are exceptionally rare.
Good luck with you case.
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