According to the Web of Knowledge, the H-index of the Bulgarian Academy of Sciences as of September 13, 2019 is 202. This means that 202 scientific papers of researchers at the Academy have been cited at least 202 times. For comparison, the H-index of Bulgaria is about 260.

The H-index has been introduced to evaluate the scientific achievements of individual scientists but has recently been increasingly used to evaluate both the relevance of various fields of science as well as scientific institutions. Although it does not take into account a number of factors such as different average citation of the individual sciences, the H-index provides an overview of the impact of an institution.

You can see the lists in Bulgarian and English here.