Can I be deported if I was born in Mexico but my father is a US citizen?

You need to speak with a qualified immigration attorney for an in depth analysis of your current and past immigration history.

You are, likely, a U.S. citizen from birth. However, you have to prove it. In a large measure, the difficulty of establishing your citizenship depends on whether your parents were married at the time of our birth: if they were not legally married, demands of proof are much harder. Let me continue this answer on an assumption that your parents were legally married at the time of your birth. Do not disregard your Mexican birth certificate as a piece of evidence in your favor: if it states your father's paternity, it makes almost a half of your case (if your birth certificate does not name your father, you have a problem) You also need - proof of your father's U.S. citizenship, - marriage certificate of your parents; and - proof that your father resided in the U.S. for not less than 5 years before you were born (at least 2 years out of these 5 had to be after your father's 14th birthday). If you don't have these documents, they can be found in the archives of the municipalities where your father lived, where your parents got married, and in the national archives (for example, you can prove that your father lived in the U.S. for 5 years as required, if you obtain his tax returns and Social Security records for those years).

If your father was a US citizen, your birth should have been registered with the US Embassy in Mexico prior to your coming to the US. If that was not done at the time, you should still be able to show your status by presenting your father's proof of citizenship in the US.

You can be deported if you can not show the necessary proof that you are became an automatic citizen through your Father. Meet with an Immigration Attorney who can help you find the documents you need and tell you the possible options for the best way to forward.

You may be a US citizen by birth under INA section 301(g) if: (1) your father was married to your mother at the time of your birth and (2) your father was physically present in the US or US possession for at least 5 years prior to your birth, two of which was after the age of 14. You can obtain proof of your citizenship by applying for a Certificate of Citizenship on form N-600 with USCIS or apply for your US passport with the Department of State.

You need to obtain proof of your US citizenship as soon as possible. You may want to start by applying for a US passport, and you need to find copies of your father's birth and death certificate and hopefully a copy of your birth certificate as a US citizen born abroad. The US consulate should have issued this to your parents.

More information is needed, but it sounds like you're a US citizen and need to claim your citizenship. It's a good idea for you to meet with an immigration attorney to discuss your situation.