Should I mention a published paper in a disreputable journal in my resumé for admission to a PhD scholarship? I want to be admitted to PhD studies at a foreign university with a scholarship.

I was in a team of four members authoring a paper, whose senior member (who is a professor) corresponded the publication himself from initial to final stage without letting us know the journal name. After the acceptance, he told us the journal’s name and we found that it is not listed in Thomson Reuters / ISI and its claim of an impact factor is fake. It is not even showing a DOI of the paper. Now we are thinking as if our whole struggle was useless.

Please advise whether I should mention the paper on my resumé for PhD scholarships admissions or not.
I understand your conflict.  On the one hand, you have produced a manuscript detailing your hard work.  On the other hand, you don't want to appear associated with a fake/predatory/otherwise questionable journal.

My suggestion is that you do include this work in some form in your CV. For example, you might have a few sections:

1) Peer-reviewed publications

2) Publications in-press

3) Other work / manuscripts / manuscripts in progress, etc.

If it were me, I might consider including this paper under #3, potentially withholding the journal name if I felt so strongly as to question whether it might even be called a journal.  Alternatively, you might include a note underneath that line item stating "submitted to non-peer reviewed journal without author's knowledge".  While this would be fairly strange to see, it would at least offer a discussion point, while giving you credit for work performed.