I very strongly advise you to consult with an immigration attorney in your area ASAP. There are many great attorneys in Austin and I'm sure many offer free consultations. It is important that you speak with attorney in person ASAP because the longer your fiance is in the country illegally, the worse the potential consequences & the more difficult it will be for you guys to overcome the issue...
It's not clear from your description what's going on in your lives...you say he has been living/working in the US for 3 years...but you also indicate that his 6 month TOURIST visa just expired. Again, talking to an attorney in person, in a confidential setting, will be a much better way for you to get advice for your specific situation...much better than sharing this very personal information on a public forum like this.
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You are risking your fiance being put in removal at any time. You should seek the help of a good reputable immigration lawyer in your area to evaluate your options and advise you accordingly. Is it possible to get married sooner than the next year? Good news is, family based immigration is more favorable to situations like yours, as long as he was examined at entry and entered the country legally. Good luck.
If you are an American citizen and marry your fiancé, you can file a petition for him and, since he entered the country legally,even if he is not legal now, he can concurrently file I-485 to adjust his status. If you wait until next year, you are risking his being picked up by immigration and placed in removal proceedings which would complicate things considerably. I also think that you should consult an immigration attorney.
I am a lawyer, but I am not your lawyer (unless you have been in my office and signed a contract). This communication is not intended as legal advice, and no attorney client relationship results. Please consult your own attorney for legal advice.
If your fiance entered the US with a visa and you are a U.S. citizen, then you may be able to adjust his status in the US once you are married (assuming he qualifies in all other respects). If you are a Lawful Permanent Resident, then his expired visa alone will not be enough to allow him to adjust his status in the US. If you are a Lawful Permanent Resident, you may want to consider naturalizing to become a US citizen (if you qualify) so you can adjust his status. If you cannot become a citizen, he may have to do consular processing to get his residency once you are married (if he qualifies for consular processing).
I think that you should consult with an experienced immigration lawyer as soon as possible so you can begin to plan out how you are going to get your fiancee his residency. There is not enough information in your post to give you a complete answer to your question. Many different issues that you did not cover (crimes, previous unlawful presence, etc.) will need to be analyzed before an attorney can tell you what you can do about your fiancee's immigration status. That is why it is very important you seek the counsel of an experienced immigration attorney.
I recommend that you do not file any application without the aid of an immigration attorney. He entered with a visa, so if you are a U.S. citizen, there is likely no problem with INA 245(a) or (c), but there very well may be a problem with INA 212(a)(9)(B) based on the fact that tourist visas are usually granted for ten years and he has only been in the U.S. (this time) for 3 years. I am very concerned about the other 7 years (and any prior visa), and furthermore would never file for you without evaluating every area of inadmissibility, along with waivers to inadmissibility.
The preceding statement was generalized information only and cannot be relied upon the same way legal advice in an attorney-client relationship can be. For individual case analysis, please contact me or another licensed attorney.