Scientifically and genealogically, it is impossible to prove that the direct bloodline of King David still exists today. Because Jewish genealogical records prior to the Roman destruction of the Second Temple in 70 C.E. were lost, no one can produce an unbroken, unquestionable paper trail. Reddit +2

While historical and genetic verification is out of reach, there are several cultural claims, traditions, and statistical probabilities surrounding David’s lineage:

• Rabbinic Families: Several prominent rabbinic dynasties, such as the Dayan family of Aleppo, Syria, maintain traditional family trees tracing their paternal ancestry straight back to Davidic kings. Messianic Bible +1
• Scholarly Lineages: Many families (including the Maharal of Prague and medieval scholar Rashi) trace their lineage to David. Because of the interrelated nature of Ashkenazi Jewish genealogy, this tradition is widely shared among many Jewish families today. Aish.com +2
• The Ethiopian Monarchy: The Solomonic dynasty of Ethiopia officially claimed that their royal line originated from the union of King Solomon and the Queen of Sheba.Reddit
• Statistical Probability: Genealogically speaking, King David lived nearly 3,000 years ago. Statistically, it is likely that millions of people spread across the Middle East and Europe share his DNA purely through the natural branching of human ancestry over the millennia. Reddit

For a deeper look into the historical and rabbinic sources exploring this heritage, you can read more via the Wikipedia Davidic Line overview or explore rabbinic source breakdowns on JewishGen.