Jesus of Nazareth inherits the right to the throne through Joseph, the husband of his mother and his adoptive father. No-one else claimed the child.
The genealogy stated in Matthew's gospel follows the royal line and the crown rights.
No-one else could claim the crown rights by natural generation due to God's prohibition - the curse on Jeconiah (see Jeremiah 22:28-30).
All of this is documented in the public domain. None of it is secret.
The Matthew genealogy shows the crown rights not necessarily passing from father to son and not necessarily the firstborn.
The genealogy in Luke is the direct line straight from Jesus, via Joseph (his adoptive father) back to Adam.
But the royal line, for administrative reasons, does not necessarily follow the direct line. This can be seen, for example, in the Kings and Queens of England and even today there will be discussions about the throne (perhaps) missing a generation and passing directly to the grandson, rather than the firstborn son. This is quite normal.
And, constitutionally, this is not, primarily (in England) a matter only for the Royal family to decide. Constitutionally, others have a say in this. Again, this is quite normal and was so, also, in Israel and, more particularly, in Judah.
Thus Luke's genealogy is the direct line. Matthew's is taken from Jewish records and is the royal line, with the missing generations as required by Jewish law.
Due to religious arguments these simple facts are disputed.
But to the unprejudiced mind they will be seen to be thoroughly logical.