From this sentence, it is very difficult to achieve that meaning (though probably not impossible). But with just a little effort and minimal changes you can do this: "Babam benim, doktor". This would help remove the confusion because -im in "benim" can't be interpreted as the possessive suffix now. This is still not the optimal solution despite the comma, but with the right context, that would work:
Doctor: "Senin baban kim?" (Who is your father?)
Me: "Babam benim, doktor".
Obviously, as the speaker would be aware of the problem of miscomprehension, he would more likely to say "Ben babamım, doktor" (I am my father) or even more explicitly "Ben kendimin babasıyım" (I am the father of myself).