Soft Kitty is a children's song that Sheldon's mother sings to him when he is sick.
The lyrics to the song are Soft Kitty, Warm Kitty, Little Ball of Fur. Happy Kitty, Sleepy Kitty, Purr, Purr, Purr.
The song was first established in the Season 1 episode of The Big Bang Theory, "The Pancake Batter Anomaly", when Sheldon came down with the flu. Sheldon asked Penny to sing the song for him as his mother used to sing it to him as a child. Penny didn't know the song, so Sheldon taught her the words.
The song was first performed on Young Sheldon in the Season 1 episode, "A Sneeze, Detention, and Sissy Spacek" when Sheldon's extreme efforts to avoid the flu turned out to be for nought.
When Sheldon was in the hospital in "A Tummy Ache and a Whale of a Metaphor", he asked Nurse Robinson to sing Soft Kitty to him when he was having trouble falling asleep.