My father who has become a U.S. citizen was arrested on charges that he went to jail 15 years ago, can he be deported

Your father should immediately retain a qualified attorney.

If he is an US citizen, the government cannot deport him until his US citizenship is revoked.

Among other bases, his US citizenship can be revoked if he obtained it by fraudulent means.

For example, if whatever he did 15 years ago make him eligible for deportation/removal but he did not disclose whatever he did when he applied for citizenship, the government may have a basis to revoke his US citizenship.

Immigration proceedings can move very fast, especially if the person is talked into signing waivers for hearings to be conducted. Someone should let your father know not to sign anything without advice from his attorney.

Without knowing more about the situation, no one can comment specifically about the situation. For help that is specific to your father's situation, he may want to review his facts and options with an attorney.

If he is a U.S. citizen, there is no place to deport him to - this is his home country...UNLESS his citizenship was obtained through fraud (such as his failure to disclose the conviction 15 years ago...it's possible). You should contact a qualified immigration attorney to sort this out.