  In this work, we studied four types of cosmological models with different
mechanisms driving the accelerated expansion of the universe, include
Braneworld models, Chaplygin Gas models, Emergent Dark Energy models, and
cosmological torsion models. Considering that the dynamics of these models at
low redshifts are very similar and difficult to distinguish, we used the latest
and largest UV and X-ray measurements of quasars (QSOs) observations covering
the range of redshift $0.009<z<7.5$. However, the high intrinsic dispersion of
this sample and the degeneracy between cosmological model parameters, we added
2D-BAO and 3D-BAO datasets to help us constrain the parameters of these
cosmological models. Our results suggest that standard cold dark matter
scenario may not be the best cosmological model preferred by the high-redshift
observations. The Generalized Chaplygin Gas (GCG) and cosmological constant
plus torsion (named Case II) models perform best by Akaike Information
Criterion (AIC), but the $\Lambda$CDM is the best cosmological model preferred
by Bayesian Information Criterion (BIC). Our work also supports that the
Phenomenologically Emergent Dark Energy and cosmological torsion models may
alleviate the Hubble tension, the reported value of the Hubble constant
obtained from QSO+BAO datasets combination lies between Planck 2018
observations and local measurements from the SH0ES collaboration, while other
cosmological models all support that the Hubble constant tends to be closer to
recent Planck 2018 results, but these model are penalized by information
criterion.
