In short
Matthew uses the term gennao to stress the bloodline of Jesus on the side of his human father, Joseph, who is a descendant of Abraham. Matthew mentions Judah’s brothers to make the connection of Jesus to the whole nation of Israel, into which Christ was born (see 1 Chronicles 2:1).
The repeated use of the Greek word gennao amplifies that the emphasis here falls on genetic lineage. In Matthew 1:16 Joseph is mentioned as a biological descendant of the aforementioned. Judah’s brothers are also mentioned alongside him since they also belong to the holy people of Israel into which Christ was born according to the flesh (see 1 Chronicles 2:1).1
2 Abraham was the father of Isaac, and Isaac the father of Jacob, and Jacob the father of Judah and his brothers,