In scenarios that stabilize the electroweak scale, the top quark is typically accompanied by partner particles. In this work, we demonstrate how extended stabilizing symmetries can yield scalar or fermionic top partners that transform as ordinary color triplets but carry exotic electric charges. We refer to these scenarios as hypertwisted since they involve modifications to hypercharge in the top sector. As proofs of principle, we construct two hypertwisted scenarios: a supersymmetric construction with spin-0 top partners, and a composite Higgs construction with spin-1/2 top partners. In both cases, the top partners are still phenomenologically compatible with the mass range motivated by weak-scale naturalness. The phenomenology of hypertwisted scenarios is diverse, since the lifetimes and decay modes of the top partners are model dependent. The novel coupling structure opens up search channels that do not typically arise in top-partner scenarios, such as pair production of top-plus-jet resonances. Furthermore, hypertwisted top partners are typically sufficiently long lived to form top-partnerium bound states that decay predominantly via annihilation, motivating searches for rare narrow resonances with diboson decay modes.