The second one is generally correct and what we typically use, ir refers to falling on the stairs and tumbling/crashing/sliding/rolling down the stairs towards the bottom or the next lower landing. Falling of the stairs can occur and would generally be used to describe someone or something that fall off the stairs and crashed to the floor below, but not by first rolling down the actual steps. People generally fall down the stairs. But in action movies they fall off the stairs, like wise in construction accidents a person could fall off the stairs. https://www.youtube.com/shorts/kZXx0CGWpt8 This person is falling down a staircase, but the American narrator says how to fall off a staircase https://www.youtube.com/shorts/Wii_1C3g47g this person fall down the staircase but the American narrator says he fell down. https://www.youtube.com/shorts/XhbEXdP6Cis this person is dropping of the staircase. it seems like YouTube accepts falling down the stairs and falling of the steps to give videos of people falling down stairs. It also seems that a significant number of Americans say falling of the stairs and that possibly the language is evolving so that they both now mean the same.

“ fell down “ is correct. We use this Term generally when referring to stairs. This will communicate that sally fell/ tumbled / rolled in a downwards motion ( on the stairs ) towards the floor “ fell off “ would be accurate for falling as well ( not for what you want to communicate here ). It will communicate that someone fell from their original location or position to another Example Sally fell off her chair Sally fell off the platform Sally fell off her bike

First one is incorrect. Only the second one makes sense