A variety of a species that exhibits the same trait after several generations of self-fertilization is called

Pure breeding line

Explanation:

A pure breeding line is a variety of a species that is homozygous for the gene of the trait under study. These pure lines produce progeny of their own kind after repeated self-fertilization as they do not have dissimilar alleles of the gene to segregate during gamete formation. For instance, a pea plant with genotype TT would produce all the progeny with the "TT" genotype after several rounds of self-fertilization as it is true to its own type.