We study the twisted elliptic genera of 2d $(0,4)$ SCFTs associated to the BPS strings in the twisted circle compactification of 6d rank-one $(1,0)$ SCFTs. Such objects can arise when the 6d gauge algebra allows outer automorphism, thus are classified by twisted affine Lie algebras. We study several fascinating aspects of twisted elliptic genera including 2d localization, twisted elliptic blowup equations, Higgsing and spectral flow symmetry. We derive a recursion formula with respect to the number of strings to exactly compute the twisted elliptic genera. We also investigate the modular bootstrap of twisted one-string elliptic genera and find certain $Gamma(N)$ modularity naturally exists with possible $N=2,3,4$. Geometrically, our study solves the BPS invariants of underlying genus-one fibered Calabi-Yau threefolds with $N$-section. This is based on a joint work with Kimyeong Lee and Xin Wang.