  In this paper, we use a newly compiled sample of ultra-compact structure in
radio quasars and strong gravitational lensing systems with quasars acting as
background sources to constrain six spatially flat and non-flat cosmological
models ($\Lambda$CDM, PEDE and DGP). These two sets of quasar data (the
time-delay measurements of six strong lensing systems and 120
intermediate-luminosity quasars calibrated as standard rulers) could break the
degeneracy between cosmological parameters ($H_0$, $\Omega_m$ and $\Omega_k$)
and therefore provide more stringent cosmological constraints for the six
cosmological models we study. A joint analysis of the quasar sample provides
model-independent estimations of the Hubble constant $H_0$, which is strongly
consistent with that derived from the local distance ladder by SH0ES
collaboration in the $\Lambda$CDM and PEDE model. However, in the framework of
a DGP cosmology (especially for the flat universe), the measured Hubble
constant is in good agreement with that derived from the the recent Planck 2018
results. In addition, our results show that zero spatial curvature is supported
by the current lensed and unlensed quasar observations and there is no
significant deviation from a flat universe. For most of cosmological model we
study (the flat $\Lambda$CDM, non-flat $\Lambda$CDM, flat PEDE, and non-flat
PEDE models), the derived matter density parameter is completely consistent
with $\Omega_m\sim 0.30$ in all the data sets, as expected by the latest
cosmological observations. Finally, according to the the statistical criteria
DIC, although the joint constraints provide substantial observational support
to the flat PEDE model, they do not rule out dark energy being a cosmological
constant and non-flat spatial hypersurfaces.
