There appears to be an understanding that the Yehi Ratzons following Torah reading are said only on Mondays and Thursdays (see for example, the Artscroll Siddur).  Halacha Lemaaseh, is this the case (sources please)?  The Nafka Minah would be a fast day that falls out on S/T/W/F.

I realize that at https://judaism.stackexchange.com/questions/64385/why-are-the-yehi-ratzon-prayers-connected-to-tachanun it is indicated that there is something special about Mondays and Thursdays, however a similar argument could be made for Fast Days, when we say Selichos, or we could just not Pasken like the view brought there.