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Simple Summary: This study investigated the family structure, parent–child pair and inbreeding coefficient of a Tan sheep breeding farm in Ningxia, China. The results can be used as the theoretical basis for selecting excellent breeding stock and making an apposite mating plan; furthermore, it can provide an important scientific basis for the conservation and reproduction of Tan sheep germplasm resources. Tan sheep is a special breed of locally protected sheep in China, one of the best quality meat sheep in the world. Due to the unclear pedigree of the rams on the Ningxia Tan sheep breeding farm, we investigated 74 rams in the field and explored a new method for family division. Genomic DNA was extracted from the blood of breeding rams. Using Plink software, GCTA tools and R language, we analyzed the genetic structure, kinship, and inbreeding coefficient of the breeding sheep, which revealed the genetic relationship between the individuals. The results showed that there was no obvious clustering phenomenon in the PCA, and the genetic background of the samples was similar. The G matrix and IBS distance matrix indicated that most individuals were far away from each other. Paternity testing identified 24 pairs of unknown parent–child pairs, and all the Tan sheep could be divided into 12 families, which provided a reference for sheep breeding. The average inbreeding coefficient based on the ROH of this population was 0.049, so there was a low degree of inbreeding and the rams in the field were able to maintain high genetic diversity. Overall, we explored a more accurate method through paternity and kinship analysis; it provides a scientific basis for pedigree construction, which has an important application value for Tan sheep breeding. [ABSTRACT FROM AUTHOR]