It was reported in Faydh Al-Qadeer which was a book of interpretation of the ahadeeth of Al-Jaami’ As-Sagheer, which was authored by As-Suyooti.
The hadeeth which you mentioned was reported by As-Suyooti in this book. and he marked it as Da’eef (weak).
Shaykh Al-Albaani classified it as Dha’eef (weak) in Dha’eef Al-Jaami’ As-Sagheer, he pointed out in Silsilatul Al-Ahaadeeth Adh-Dha’eefah wal-Mawdhoo’ah that it had become clear to him that it was a fabricated hadeeth, as he said,
“Al-Munaawi mentioned the hadeeth in Sharh Faydh Al-Qadeer and in Sharh At-Tayseer, but he did not comment on it; whereas the rule with regard to such a hadeeth is to classify it as Dha’eef. This is what I did in Dha’eef Al-Jaami’ [i.e. I classified it as Dha’eef]. And now, as I came to know about its obscure chain of narrators and pondered about its wording, it has become clear to me that it is a fabricated hadeeth.”
About Mustradak Al Hakim, I couldn't find if the hadith was mentioned in there but if it was, it would be da'eef(weak) anyway as quite a lot of the Mustradak Al Hakim has fabricated hadith as al-Dhahabi said:
"The Mustadrak contains a good number of hadîth that conform to the conditions of authenticity of both (al-Bukhârî and Muslim) as well as a number of hadîth conforming to the conditions of either one of them. Perhaps the total number of such hadîth comprises half the book. There is roughly another quarter of the hadîth that have authentic chains of transmission, but that have something else about them or that have some defect. As for the rest, and that is about a fourth, they are rejected and spurious narrations that are unauthentic. Some of those are fabrications. I came to know of them when I prepared an abridgement of the Mustadrak and pointed them out."