All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Your question is not quite clear for us to give a clear answer yet after intensive research in various books, we did not find such a phrase like "Faatimah's hand" as a separate term. Imaam Al-Bukhari and Muslim however, narrated a Hadeeth (narration) on the authority of Faatimah bint Qays who had said, "The Prophet (peace be upon him) said about a woman who is divorced three times: 'She is neither entitled to housing nor expenditure.'"
In Nayl Al-Awtaar (The Achievement of Goals), Ash-Shawkaani said, "Ad-Daaraqutni said, 'The Sunnah (knowledge of the Prophet's sayings and traditions) is in the hand of Faatimah [meaning she was right in what she had said about the Hadeeth aforementioned].'"
He (Ad-Daaraqutni ) said that based on the fact that the Prophet's Companions all, differed among themselves as to whether a woman who is divorced three times is entitled to obtaining the right of housing and expenditure.
Some of them were of the opinion that she has right to neither housing nor expenditure. Yet some others were of the opinion that she has such a right. Faatimah bint Qays held the first opinion based on the previously mentioned Hadeeth that she narrated from the Prophet, .
Thus, dear questioner, if this is not what you are asking about, then please rewrite to us making your question more understandable for us to give you a proper answer.
Allaah Knows best.