High-redshift radio sources provide plentiful opportunities for studying the formation and evolution of early galaxies and supermassive black holes. However, the number of known radio-loud active galactic nuclei (AGN) above redshift 4 is rather limited. At high redshifts, it appears that blazars, with relativistically beamed jets pointing toward the observer, are in the majority compared to the radio-loud sources with jets misaligned with respect to the line of sight. To find more of these misaligned AGN, milliarcsecond-scale imaging studies carried out with very long baseline interferometry (VLBI) are needed, as they allow us to distinguish between compact-core-jet radio sources and those with more extended emission. Previous high-resolution VLBI studies revealed that some of the radio sources among blazar candidates in fact show unbeamed radio emission on milliarcsecond scales. The most accurate optical coordinates determined with the Gaia astrometric space mission are also useful in the classification process. Here, we report on dual-frequency imaging observations of 13 high-redshift (4 < z < 4.5) quasars at 1.7 and 5 GHz with the European VLBI Network. This sample increases the number of z > 4 radio sources for which VLBI observations are available by about a quarter. Using structural and physical properties, such as radio morphology, spectral index, variability, brightness temperature, as well as optical coordinates, we identified six blazars and six misaligned radio AGNs, with the remaining one tentatively identified as blazar.