  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.
