First off, the Southern and Northern split to which you're referring applied to Israel a few centuries before Roman occupation. The kingdom split, according to the Bible, after the reign Solomon. The southern kingdom was called Judah while the northern retained the name Israel. Then the Assyrians attacked the northern kingdom and scattered the inhabitants. The Babylonians did the same to the southern kingdom. The Samaritans did descend from the northern tribes, but that has nothing to do with their eventual location on the Roman territory map.

During the Roman empire at the time of Jesus, Jews could be found all over the place. However, as far as Jewish territories go, when Jesus was born, there was only one: the Herodian Kingdom of Judea. The kingdom of Judea included Nazareth and Jerusalem. However, when Herod died, the kingdom was split into a tetrarchy, divided among four other rulers. This was when Galilee was handed off to Herod Antipas while Herod Archelaus ruled Judea (which included Samaria). But Archelaus was not a good leader, so Rome deposed him and Judea became a strict Roman province with a Roman governor.

By the time Jesus was grown, the differences between Galileans and Judeans were stark, but they had nothing to do with the Jewish identity. Instead, there Galileans were viewed as backwards hillbillies, basically, and Judeans made fun of their accents all the time. This is why the statement is made about Jesus, "Can anything good come out of Nazareth?"

I really encourage you to read some of the great work done by R. T. France, such as his commentary on Matthew. I hope this had helped.

The background of Jesus, and even of Galilee, can be a bit contentious. One of the most famous Galileans, besides Jesus, was this figure named Judas of Galilee, that we learn of from Josephus. Judas's story has an interesting connection to Jesus. In Luke, the author talks about a census. Simply, Luke gets the census wrong. He places it at a wrong time (and adds aspects that never happened). But that census occurred around 6 C.E., and it spurred a rebellion, which Judas of Galilee was one of the leaders.

Josephus tells us that Judas and another figure named Zadok the Pharisee, started a fourth philosophy in Judaism. That philosophy was the Zealots. They were a bit more, well zealous in nature.

I mention that because a lot of earlier historians equated Galilee with the Zealots. In Albert Schweitzer's classic book, the Quest for the Historical Jesus, you see in the late 19th century, and up to that point, this was a major view within the scholarship.

A big readjustment in Judaism, or our understanding of Judaism, happened with E.P. Sanders. He has a great work where he really explores Palestinian Judaism, really dives into the subject in other books such as his work on Jesus and Judaism. One thing that Sanders does is examine what Palestinian Judaism really looked like, and it wasn't that everyone from Galilee was a Zealot. Instead, Sanders argues that Jesus was fully Jewish, and was working with the Jewish eschatology ideas of that time. Basically, Jesus was a Palestinian Jew.

But we do have to step back just a bit. Geza Vermes, alongside Sanders, is a scholar who really helped increase the understanding of what Judaism was during the time of Jesus, and how it interacted with Jesus. Vermes has two excellent works on this, Jesus and the World of Judaism, and the Religion of Jesus the Jew. What Vermes points out is that there was most likely some chauvinism, as he says, in Galilee. It's a trait they are known for. Part of this may be propaganda against them, but it seems as if there is some real basis for this. We see this directly in the Gospels with how Jesus interacts with others, such as calling a Gentile woman a dog and telling his disciples not to mention with Gentiles. Jesus also states that his disciples should not enter the cities of the Samaritans.

Even his story about the good Samaritan, it only makes sense if Samaritans are seen as lower. And as Vermes points out, it is likely that a few of the followers of Jesus were Zealots. It matches with the eschatological view Jesus was preaching.

So what we can be sure of is that Jesus was not a Samaritan. He was what we would call a Palestinian Jew, and specifically, a Galilean Jew. Jonathan L Reed, dives into this subject in an interesting manner. He uses archaeology to see what this would mean. One thing that Reed points out is that Galilean Judaism was different from Judea Judaism. In Galilee, the Jews are at a distance from the Temple. They are removed from the center of the religion, and that's going to effect how they believe. At the same time, in Galilee, there are some great Roman cities being built, and the Hellenization process is starting to expand. This was often seen as a danger to the Jewish way of life. That's why in Galilee, in the first century, we see the rise of people like Judas of Galilee with a physical rebellion, and people like John the Baptist and Jesus, who are preaching a coming Kingdom of God that will replace the current Kingdom of Rome.

That background can help explain why Galileans were seen as Zealots, and why the Zealot movement formed there. But we need to circle back to the second leader of the Zealot movement, Zadok the Pharisee. Zealots and Pharisees seemed to be connected. And it brings up a very interesting possibility, that Jesus was himself a Pharisee. This may seem like a weird proposal, because the Gospels are pretty down on the Pharisees, but as John Dominic Crossan explains in Who Killed Jesus, that is more likely due to polemic against Rabbinical Judaism, which derives from the Pharisees. After the Temple destruction in 70 CE, and after the first Jewish War ended, the only Jewish sects left were the Pharisees, which became Rabbinical Judaism, and Jewish Christians, which would become Christianity. And the two had quite a bit of polemic against each other, and it was in that environment that the Gospels were written. Before that, Pharisees weren't seen in a negative light. After all, Paul was a Pharisee.

Really examining this, Rabbi Harvey Falk, in Jesus the Pharisee, looks at what Jesus taught, and compares it to Jewish ideology of that time. Falk argues that the debates between Jesus and the Pharisees should be seen as something happening within Pharisaism, that it was inter-Pharisee disputes. It was simply part of the form of Judaism. For instance, we have the century long dispute between two Pharisee schools of thought, that of Hillel and Shammai. Falk also looks at how the Pharisees, and especially the Shammai school, was working with the Zealots. That they were connected.

For Jesus though, it appears that he was more of the Hillel school of thought, and even the summary of the law that Jesus teaches is exceptionally similar to that which Hillel taught.

The idea that Jesus was a Pharisee has taken off a bit more in recent times, but it is still debated.