The aim of the study was to determine the prevalence of ESBL/AmpC-producing Escherichia (E.) coli and to investigate their on-farm distribution on an exemplary dairy farm. For this purpose, sample sizes were calculated, and fecal samples were collected from cattle of all ages and analyzed for the presence of ESBL/AmpC-E. coli using selective media supplemented with cefotaxime. These antibiotic-resistant bacteria were detected in 22.5% of the samples tested. The prevalence was highest in the calf age group, in which 100% of the collected fecal samples were positive. With increasing age, the prevalence decreased in the other sample groups. While ESBL/AmpC E. coli could still be detected in young stock (15%) and breeding heifers (5%), no resistant pathogens could be detected in adult animals. Whole-genome sequencing of the ESBL/AmpC-E. coli isolates revealed, first, that all isolates were ESBL producers (CTX-M-1 and CTX-M-15) and, second, that ST362, which is known as a biofilm producer, was dominant in the calves (85%, n = 17). Based on these results and the evaluation of a questionnaire, possible causes for the occurrence of ESBL/AmpC-E. coli were discussed and recommendations for the reduction in transmission were formulated. Unlike most German dairy farms, no waste milk feeding was apparent; therefore, factors reducing ESBL/AmpC-E. coli are primarily related to an improvement in hygiene management to prevent biofilms, e.g., in nipple buckets, but also to question the use of antibiotics, e.g., in the treatment of diarrheic calves.