  As an essential ingredient of quantum networks, quantum conference key
agreement (QCKA) provides unconditional secret keys among multiple parties,
which enables only legitimate users to decrypt the encrypted message. Recently,
some QCKA protocols employing twin-field was proposed to promote transmission
distance. These protocols, however, suffer from relatively low conference key
rate and short transmission distance over asymmetric channels, which demands a
prompt solution in practice. Here, we consider a tripartite QCKA protocol
utilizing the idea of sending-or-not-sending twin-field scheme and propose a
high-efficiency QCKA over asymmetric channels by removing the symmetry
parameters condition. Besides, we provide a composable finite-key analysis with
rigorous security proof against general attacks by exploiting the entropic
uncertainty relation for multiparty system. Our protocol greatly improves the
feasibility to establish conference keys over asymmetric channels.
