As part of the GLOSTAR (GLObal view of STAR formation in the Milky Way) survey, we present the high-resolution continuum source catalog for the regions (l = 2-28, 36-40, 56-60, &|b|<1.0), observed with the Karl G. Jansky Very Large Array (VLA) in its B-configuration. The continuum images are optimized to detect compact sources on angular scales up to 4", and have a typical noise level of 1sigma ~ 0.08mJy/beam for an angular resolution of 1", which makes GLOSTAR currently the highest resolution as well as the most sensitive radio survey of the northern Galactic plane at 4-8GHz. We extracted 13354 sources above a threshold of 5sigma and 5437 sources above 7sigma that represent the high-reliability catalog. We determined the in-band spectral index (alpha) for the sources in the 7sigma-threshold catalog. The mean value is alpha=-0.6, which indicates that the catalog is dominated by sources emitting non-thermal radio emission. We identified the most common source types detected in radio surveys: 251 HII region candidates (113 new), 282 planetary nebulae (PNe) candidates (127 new), 784 radio star candidates (581 new), and 4080 extragalactic radio source candidates (2175 new). A significant fraction of HII regions and PNe candidates have alpha<-0.1 indicating that these candidates could contain radio jets, winds or outflows from high-mass and low-mass stellar objects. We identified 245 variable radio sources by comparing the flux densities of compact sources from the GLOSTAR survey and the Co-Ordinated Radio `N' Infrared Survey for High-mass star formation (CORNISH), and find that most of them are infrared quiet. The catalog is typically 95% complete for point sources at a flux density of 0.6 mJy (i.e. typical 7sigma level) and the systematic positional uncertainty is <= 0.1". The GLOSTAR data and catalogs are available online at https://glostar.mpifr-bonn.mpg.de.Read less <