Other claimants to throne of David besides Jesus? Since Jesus was in the royal line, it seems likely he had contemporaries in the royal line also. Is it possible to estimate how many legitimate candidates for King of Israel lived at the time of Jesus, based on genealogies? Do we have any historical record of such people?
None of the seed of David, through Jeconiah, could ever inherit the throne of David due to the curse upon Jeconiah recorded by the prophet Jeremiah.
Jeremiah states of Jeconiah, king of Judah :

Thus saith the LORD, Write ye this man childless, a man that shall not prosper in his days: for no man of his seed shall prosper, sitting upon the throne of David, and ruling any more in Judah.      [Jeremiah 22:30 KJV]

Of this curse upon not only Jeconiah himself but on the succession of any king to the throne who was of that seed, Matthew Henry's commentary records the following :

Now that which is here to be taken notice of is that Jeconiah is written childless (v. 30), that is, as it follows, No man of his seed shall prosper, sitting upon the throne of David. In him the line of David was extinct as a royal line

Biblehub - Jeremiah
Thus only Jesus, the child of Mary (and the child of Mary's husband Joseph) who, alone, inherited all the rights to the throne from Joseph, but inherited none of the curse, being not of the seed of Jeconiah by natural generation.
Ellicott also comments :

The meaning of the prediction, as explained by the latter clause of the verse, was fulfilled in Jeconiah’s being the last kingly representative of the house of David, his uncle Zedekiah, who succeeded him, perishing before him (Jeremiah 52:31). In him the sceptre departed, and not even Zerubbabel sat upon the throne of Judah.

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