We are hearing the story of bibi Sayyeda SA that she used to get tired in household chores so maula Ali AS sent her to her baba to ask for a Kaneez and then rasool e khuda gave her the tasbeeh. How true is this?

Yes it is a true fact that the Holy Prophet (s.a.w) granted this form of recitation to His beloved daughter Hazrat Fatema (s.a) and declared it to be better than a maidservant and in fact and whole world and what is in it. You can find out of its merits in dua.org by typing significance of the tasbeeh.