I am wondering if one can use energy or vitamin patches on fast days, or such patches on Pesach if they contain kitniyot.
To the Questioner,
Since only eating and drinking is prohibited on fast days (OTHER than Yom Kippur and Tisha B'av), and there is no qualified scientific evidence for absorption of vitamins through the skin (see: https://www.mercurynews.com/2018/09/05/do-vitamin-patches-actually-work/), it would not be prohibited on the regular fast days - just as applying anything else to the skin is not prohibited.
On Yom Kippur and Tisha B'av, however, when smearing of the skin in a pleasurable way is prohibited, they should not be used.
On Pesach, the minhag of Ashkenazim not to partake of kitniyot applies specifically to eating or drinking; there is no minhag to refrain from benefitting from kitniyot.
Therefore, if all the other ingredients are kosher for Pesach, they would be able to be used.