Elemental abundances of extrinsic carbon stars provide insight into the poorly understood origin and evolution of elements in the early Galaxy. In this work, we present the results of a detailed spectroscopic analysis of four potential carbon star candidates from the Hamburg/ESO Survey (HES): HE 0457-1805, HE 0920-0506, HE1241-0337, and HE 1327-2116. This analysis is based on the high-resolution spectra obtained with Mercator/HERMES (R~86000) and SUBARU/HDS (R~50000). Although the abundances of a few elements, such as Fe, C, and O, are available from medium-resolution spectra, we present the first ever detailed high-resolution spectroscopic analysis for these objects. The objects HE 0457-1805 and HE 1241-0337 are found to be CEMP-s stars, HE 0920-0506 a CH star, and HE 1327-2116 a CEMP-r/s star. The object HE 0457-1805 is a confirmed binary, whereas the binary status of the other objects is unknown. The locations of program stars on the diagram of absolute carbon abundance A(C) versus [Fe/H] point at their binary nature. We have examined various elemental abundance ratios of the program stars and confirmed the low- mass nature of their former AGB companions. We have shown that the i-process models could successfully reproduce the observed abundance pattern in HE 1327-2116. The analysis performed for HE 0457-1805, HE0920-0506, and HE 1241-0337 based on the FRUITY parametric models confirmed that the surface chemical compositions of these three objects are influenced by pollution from low-mass AGB companions.