I recently took my Ph.D qualification exam. Out of the 4 exams I took, I passed 3 and I failed one. My professor failed me because I failed the written one and because of that, I failed the oral exam too. I asked my professor if I can see the written exam, and I found out that there were 2/3 questions I answered right, but he marked it wrong. I showed that to him and he said he is not going to change the score. I do have a chance to retake the exam later, but now I am bit afraid, If I retake it, is he going to do the same again on the new exam. Any advice would help
It is your characterization that the evaluation is unfair. An alternate explanation is that it was a judgement call and that overall, the prof decided you weren't well enough prepared.
I can't make a judgement call here, of course, but in reality, you may not be very successful with an additional appeal - especially if it is confrontational.
My best advice is to study hard for the re-take and do well enough so that any judgement calls are in your favor. If you can arrange for an oral exam with more than one professor, however, you are at least partially protected from any bias. You might even be justified in asking for a different examiner.
If this were the last attempt at the exam, you might need to worry about appeals and such. But most of your faculty would probably suggest that you just do what it takes to pass. You aren't likely to get a pass when you have open the option of a retake.
It is not clear what you want advice for. You could try to rephrase your question.
Moreover, we can not really help you as we don't know the professor and also not the institution.
In some places, you could appeal the exam by going to higher ranked people, in other places, students appealing are always ignored. It could be possible that you do the exam with another professor or not, that he does the same in the next exam or not, but we cannot say.
My advice: Talk to people which know both the professor and your institution. (For example, your student union.) Ask them if you can do something and if yes, what.
(For what it's worth, while I've met some blanantely unfair professors (women shall not pass the exam; after the exam no points will be added if there where errors in the marking), most professors listen to reason.)