One thing that I found disturbing in comments for this question is to read that God was the father of Jesus. For Christians, it is blasphemous to say that God had a son. Jesus being called the Son of God was to portray that Jesus was same in likeness as God which meant that He was God incarnate.
Regarding lineage of Jesus it just a notional that Jesus was assigned to an earthly father and mother. Jesus was prophesied to come to a family with a lineage link to king David. Gospel of Mathew gives us the lineage of Jesus from David towards Joseph and Luke gives the lineage of Jesus from David towards Mary.
Mathew is indicating that Joseph is from David through Solomon and Luke is indicating that Mary is also from David through Nathan. That is why we see differences in the lineages given by Luke and Mathew. Luke’s lineage is thru Jesus maternal grandfather Eli.
Luke’s text says that Jesus was “a son, as was supposed, of Joseph, of Eli”. This been understood as acknowledgment of the virgin birth. The parenthetical expression: “a son (as was supposed of Joseph) of Eli” indicate that Jesus is called a son of Eli because Eli was his maternal grandfather, his nearest male ancestor on His mother side. A variation on this idea is to explain “Joseph son of Eli” as meaning a son-in-law, perhaps even an adoptive heir to Eli through his only daughter Mary. An example of the Old Testament use of such an expression is Jair, who is called “Jair son of Manasseh” but was actually son of Manasseh’s granddaughter.