Q: Can one fast a qada (missed) fast or any optional fast on a Friday?
A: One should not keep a nafl or optional fast on Friday alone. Either keep fast on Thursday and Friday, or Friday and Saturday, or else choose any other week day.
If one did already observe a fast on Friday alone, then it is valid. There is no need to repeat it. However, it is better to do as explained above.
Mufti Siraj Desai