By what did Jesus call Joseph?

Answering with scripture, tradition and even with your own experience in life, you should be able to reason which of these two common terms would be preferable.

For those reading scriptures, only with faith in it being the word, shows what Christ could not say for an answer:

Mat_23:9 And call none your father upon the earth: for one is your Father, which is in heaven.

Luk 2:49 And he said unto them, How is it that ye sought me? wist ye not that I must be about my Father's business?

Joh_10:35 If he called them gods, unto whom the word of God came, and the scripture cannot be broken;

In Mat_23:9 - and Joh_10:35 - This would stand to reason in him declaring that "the scripture cannot be broken" he didn't break his own beliefs. In Luk 2:49 - This is understood he has only referenced God as father in this context, that when he uses the term Father throughout scriptures, he is always referring only to God in calling him father.

The necessity to give this reminder to his followers shows it was used then by unbelievers or oppressively, therefore not to let it be wrongly used to corrupt how God is worshiped as their Father by his children. (Can be taken literally as here, or spiritually with another interpretation, as mentioned this seen only by itself without looking at tradition.)

For those reading scriptures, in only a historic and a traditional view, what a religious son could say, for an answer:

As both being in Luk_2:41 - "his parents."

As a title by his mother in Luk_2:48 - "thy father and I."

He was recognized, growing up, by many in tradition of the Capernaum's synagogue in Joh_6:42 "the son of Joseph."

• In Luk_2:41 and Luk_2:48 - This is seen that his mother and him respectfully recognizes Joseph as his paternal father, dictating by Jewish tradition and in the commandments, to honour his parents as well, he would be taught to refer to him as such by using the common term abba used for father as Jews do today.

Adopted or a stepchild as in historical Rom_8:15 the Aramaic word abba (spiritually referred for followers in the scriptures), is used by adults as well, also towards older men, as it is today. The word Father is added after the word Abba supposedly for Greeks or non Jews clarity.

Common for Christians now, they use the word pop, papa or dad, not father. Using the name father was and is more uncommonly used by high society. Joseph being a God fearing carpenter, knew the scriptures and in them the term Father for God, as did the men in Capernaum.

The answer was part given at the end of your own question. Though simply by the scriptures Mat_23:9 - there is a problem with him calling Joseph "father" and by tradition shown used in Rom_8:15 - it is more acceptable for him to have used the same terms as other common Jewish sons did and do now.

• His parents also had the choice to raise him differently, like in a small community, Essene sect then not followed the traditions around them and have taught him to use the term father for Joseph and God. (Reason what a religious son could say.)

It would be sure Christ was faithful and honourable to both his Father and abba.

From the Scripture, there is no direct information about the question. But after reading the answers and a little bit of dig into the Bible, I can say that it is probably "Father".

And when they saw him, they were amazed: and his mother said unto him, Son, why hast thou thus dealt with us? behold, thy father and I have sought thee sorrowing. And he went down with them, and came to Nazareth, and was subject unto them: but his mother kept all these sayings in her heart. [cf. Lk 2:48-51 (RSVCE)].

At least up until the above event, it seems that Jesus may have regarded Joseph as his real father for Mary is saying "thy father and I have sought thee sorrowing" and for they didn't understand what Jesus was saying.

Also, take a look at my other question Was the virgin conception of Jesus known to the people at the time? People around Jesus didn't know the Virgin Conception of Jesus at the time. It may be because that Jesus behaved a normal son before his ministry.

As @Flimzy wrote in a comment, calling "stepfather" father isn't a strange thing anyway.

I may need to ponder further on what Jesus think about Joseph by himself, but for the specific question, I feel comfortable with "Father" as the answer.

This answer is complete speculation, as there is not much scriptural support. After reading through the gospel narratives of Jesus' childhood, I noticed a few points of interest:

• When instructing Joseph to flee Egypt and head to Israel, the angel does not refer to Joseph as the child's father:

saying, “Rise, take the child and his mother and go to the land of Israel, for those who sought the child’s life are dead.” - Matthew 2:20

• Luke refers to Joseph as the "father" in his account of them receiving Simeon's blessing.

And his father and his mother marveled at what was said about him. - Luke 2:33

• At the temple, Christ makes a distinction between Joseph and God as His Father, which leads me to believe that up until this point, he most likely referred to Joseph as his father in a colloquial sense.

And he said to them, “Why were you looking for me? Did you not know that I must be in my Father’s house?” - Luke 2:48