Can a deported person have his immigration papers fixed?

A person who has been deported from the United States may be able to receive an immigrant visa and re-enter the United States. Depending upon your specific circumstances, you could marry and have your wife petition for you to receive an immigrant visa. You will likely need to file a hardship waiver for your previous illegal presence in the U.S. and application for readmission as you were deported from the United States. Under the circumstances, it would be best for you and your girlfriend to speak with an experienced immigration attorney who can review your entire immigration history and other relevant facts and explain the process with you in greater detail.

I would need more information about how your father entered the U.S., his family ties to the country, how long he has been here, where he if from, etc. There are some forms of relief a person can seek from removal, but they require more information.