"Son" is supplied in verse 23 for all the following verses. Notice that it begins in the Greek with
υἱὸς Ἰωσήφ, τοῦ Ἡλί,
24τοῦ Ματθάτ, τοῦ Λευΐ, τοῦ Μελχί, τοῦ Ἰαννά, τοῦ Ἰωσήφ,
25τοῦ Ματταθίου, τοῦ Ἀμώς, τοῦ Ναούμ, τοῦ Ἐσλί, τοῦ Ναγγαί,
26τοῦ Μαάθ, τοῦ Ματταθίου, τοῦ Σεμεΐ, τοῦ Ἰωσήφ, τοῦ Ἰούδα,
27τοῦ Ἰωανάν, τοῦ Ῥησά, τοῦ Ζοροβάβελ, τοῦ Σαλαθιήλ, τοῦ Νηρί,
28τοῦ Μελχί, τοῦ Ἀδδί, τοῦ Κωσάμ, τοῦ Ἐλμωδάμ, τοῦ Ἤρ,
29τοῦ Ἰωσή, τοῦ Ἐλιέζερ, τοῦ Ἰωρείμ, τοῦ Ματθάτ, τοῦ Λευΐ,
30τοῦ Συμεών, τοῦ Ἰούδα, τοῦ Ἰωσήφ, τοῦ Ἰωνάν, τοῦ Ἐλιακείμ,
31τοῦ Μελεᾶ, τοῦ Μαϊνάν, τοῦ Ματταθά, τοῦ Ναθάν, τοῦ Δαυίδ,
32τοῦ Ἰεσσαί, τοῦ Ὠβήδ, τοῦ Βόοζ, τοῦ Σαλμών, τοῦ Ναασσών,
33τοῦ Ἀμιναδάβ, τοῦ Ἀράμ, τοῦ Ἑσρώμ, τοῦ Φάρες, τοῦ Ἰούδα,
34τοῦ Ἰακώβ, τοῦ Ἰσαάκ, τοῦ Ἀβραάμ, τοῦ Θάρα, τοῦ Ναχώρ,
35τοῦ Σερούχ, τοῦ Ῥαγαῦ, τοῦ Φάλεγ, τοῦ Ἑβέρ, τοῦ Σαλά,
36τοῦ Καϊνάν, τοῦ Ἀρφαξάδ, τοῦ Σήμ, τοῦ Νῶε, τοῦ Λάμεχ,
37τοῦ Μαθουσάλα, τοῦ Ἐνώχ, τοῦ Ἰαρέδ, τοῦ Μαλελεήλ, τοῦ Καϊνάν,
38τοῦ Ἐνώς, τοῦ Σήθ, τοῦ Ἀδάμ, τοῦ θεοῦ.
"Son" is thus assumed in every genealogical connection although it is only supplied at the beginning of verse 23, and that is the only place it appears in this entire pericope so that what you have is "son of Joseph, of Eli,
24 of Matthat, of Levi, of Melchi, of Jannai, of Joseph,
25 of Mattathias, of Amos, of Nahum, of Hesli, of Naggai, and so on until verse
38of Enosh, of Seth, of Adam, of God.