Optimal spectral supersaturation for cliques and odd cycles

Let $Y_{n,r,q}$ be the graph obtained from the Turán graph $T_{n,r}$ by adding $q$ pairwise disjoint edges inside a largest part, and let $c(n,F)$ be the minimum number of copies of $F$ created by adding a single edge to $T_{n,r}$. Fang, Li, Lin and Ma proved that for every color-critical graph $F$