For simplicity, original code refers to the software provided by the original repository or paper, and additional code refers to what is only provided by the fork.
A good litmus test is this: Suppose you had written the additional code yourself. Would you mention this, what algorithms you used, etc. in the paper? Or would this code be part of your publication, e.g., to ensure reproducibility. If yes, you should also cite the fork.
For example, if the original code allows you to perform some simulations and the additional code is only about plotting and does not touch the actual simulations (and you checked this to a reasonable extent), do not cite the fork for the same reason that you would not mention or provide any own code or plotting library that does nothing but plot some existing data. There is no reason to assume that the original does not suffice to reproduce your results. If it considerably helped you in preparing your plots, consider acknowledging it.
If, however, the additional code modifies the original code in a way that could affect the results, cite it.
It does not matter whether the code added any functionality you used, but without this citation your work could not be reproducible anymore.
Remember that citing does not only give credit but also shifts blame.