Can I petition back my fiancée who has three charges?

More detailed information are needed about your fiancee to determine his options.

The fraud and federal charges are concerning. Generally, a U.S. citizen marrying non-citizen can petition whereby the non-citizen may legalize status. Your fiancée is seeking admission for which generally a person can have no more than one crime of moral turpitude which is generally a misdemeanour offense where the maximum sentence is one year but the individual is sentenced to no more than 6 months. If your fiancée is still facing criminal charges w/out final result then the U.S. immigration authorities will not process his case until after final decision on all pending criminal charges. Based on your brief information, your fiancée needs an immigration attorney and possibly a criminal defence attorney in order to prevent pleading to a serious offense under immigration laws whereby he would be absolutely barred from legalizing his status.

He can request voluntary departure if he is not eligible for any other form of relief. It is important to determine if he has a defense to the deportation. Meanwhile, if he marries you and you petition him, he can do consular processing. However, if he had lived in the U.S. undocumented over a year, he will have to apply for a waiver. If he indeed gets removed from the the U.S. , he will have to apply for two waivers.

I base my answer on the fact that he was in the US only one time and in excess of 180 days. So if you marry him, we can apply for waivers of unlawful presence, criminal and immigration fraud for him.