You are invoking is "Nemo judex in causa sua" (no one should be a judge in their own cause), which is a core pillar of Natural Justice. When an appellate authority has a personal or official interest in the subject matter, or when their own conduct is under scrutiny, it creates a reasonable apprehension of bias.
You can send an Application for Recusal instead of just a standard letter, formally title the document:
"Application requesting Recusal of the First Appellate Authority on grounds of Official Bias and conflict of interest."
When you cite the judgments, explicitly connect them to the facts of your situation:
A.K. Kraipak v. Union of India (1969): The Supreme Court held that the rules of natural justice apply to administrative proceedings as well. Mention that the court emphasized that the test is not whether actual bias has occurred, but whether there is a reasonable apprehension of bias in the mind of the party.
Ashok Kumar Yadav v. State of Haryana (1985): The Court reiterated that if there is a reasonable likelihood of bias, the officer must recuse themselves to ensure justice is not only done but seen to be done.If the Appellate Authority ignores your letter, goes ahead anyway, and rejects your appeals, do not worry, you can file a second appeal.When you file your Second Appeal, your very first and strongest argument will be that the First Appellate order is completely void (void ab initio) because it violated the principles of natural justice.
