  Context. While over 1000 supernova remnants (SNRs) are estimated to exist in
the Milky Way, only less than 400 have been found to date. In the context of
this apparent deficiency, more than 150 SNR candidates were recently identified
in the D-configuration Very Large Array (VLA-D) continuum images of the 4--8
GHz global view on star formation (GLOSTAR) survey, in the Galactic longitude
range $-2^\circ<l<60^\circ$. Aims. We attempt to find evidence of nonthermal
synchrotron emission from 35 SNR candidates in the region of Galactic longitude
range $28^\circ<l<36^\circ$, and also to study the radio continuum emission
from the previously confirmed SNRs in this region. Methods. Using the
short-spacing corrected GLOSTAR VLA-D+Effelsberg images, we measure ${\sim}6$
GHz total and linearly polarized flux densities of the SNR candidates and the
SNRs that were previously confirmed. We also attempt to determine the spectral
indices by measuring flux densities from complementary Galactic plane surveys
and from the temperature-temperature plots of the GLOSTAR-Effelsberg images.
Results. We provide evidence of nonthermal emission from four candidates that
have spectral indices and polarization consistent with a SNR origin, and,
considering their morphology, we are confident that three of these
(G28.36+0.21, G28.78-0.44, and G29.38+0.10) are indeed SNRs. However, about
$25\%$ of the candidates have spectral index measurements that indicate thermal
emission, and the rest of them are too faint to have a good constraint on the
spectral index yet. Conclusions. Additional observations at longer wavelengths
and higher sensitivities will shed more light on the nature of these
candidates. A simple Monte-Carlo simulation reiterates the view that future
studies must persist with the current strategy of searching for SNRs with small
angular size to solve the problem of the Milky Way's missing SNRs.
