  We investigate the behavior of various measures of quantum coherence and
quantum correlation in the spin-1/2 Heisenberg XYZ model with added
Dzyaloshinsky-Moriya (DM) and Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA)
interactions at a thermal regime described by a Gibbs density operator. We aim
to understand the restricted hierarchical classification of different quantum
resources, where quantum coherence $\supseteq$ quantum discord $\supseteq$
quantum entanglement $\supseteq$ quantum steering $\supseteq$ Bell nonlocality.
In order to enhance quantum coherence, quantum correlation, and fidelity of
teleportation, our analysis encompasses the effects of independently provided
sinusoidal magnetic field control as well as DM and KSEA interactions on the
considered system. The results reveal that enhancing the entanglement or
quantum correlation of the channel does not always guarantee successful
teleportation or even an improvement in teleportation fidelity. Thus, the
relationship between teleportation fidelity and the channel's underlying
quantum properties is intricate. Our study provides valuable insights into the
complex interplay of quantum coherence and correlation hierarchy, offering
potential applications for quantum communication and information processing
technologies.
