According to Jewish Law, is Jesus entitled to the throne of David?

Can it be shown from Jewish law/tradition that the legal right to the royal lineage may be passed through adoption, as in the case of Joseph (descendant of David) and Jesus? It's my understanding that, if Mary is descended from David, it is irrelevant to Jesus because the royal lineage is not passed through the mother but through the father only. I'm having a hard time understanding the conflicting genealogies of the Messiah. Thank you in advance for your time, God bless