I am doing mBJ calculation for a ternary semiconductor. There are
    four options for different parametrization of mBJ:

    0: Original.....
    1: New parametrization (Koller.........
    2:   New parametrization for semiconductors ........
    3: Unmodified BJ potential (Backe.........)

    I got  reasonable band gap using unmodified BJ potential, option
    3, than other options.
    My query is that: Should I put unmodified BJ potential as mBJ
    potential in paper


No

    or write simply unmodified BJ potential without mentioning mBJ
    potential?


Yes, but it should not be necessary to write unmodified. You could simply mention that you used the Becke-Johnson (BJ) potential and cite the article J. Chem. Phys. 124, 221101 (2006).
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