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.
Perhaps you mean the hadeeth reported on the authority of ʻAa'ishah which reads, "I never saw anyone more like the Messenger of Allaah in respect of gravity, calm deportment, pleasant disposition than Faatimah. When she came to visit him (the Prophet) he got up to (welcome) her, took her by the hand, kissed her and made her sit where he was sitting; and when he went to visit her, she got up to (welcome) him, took him by the hand, kissed him, and made him sit where she was sitting." [Abu Daawood, At-Tirmithi, and others - Al-Albaani graded it saheeh (sound)]
However, we could not find any report with the wording mentioned in the question, "He would spread his garment for her to sit on it."
Allaah knows best.