A global view on star formation: The GLOSTAR Galactic plane survey. VII. Supernova remnants in the Galactic longitude range $28^\circ<l<36^\circ$

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.