The Church of God claims that because Jesus and the early church members kept the Sabbath, they should too. They claim that in the Old Testament, they kept the Sabbath by killing sheep, and in the New Testament, they kept the Sabbath by preaching the Bible. Here's why they make this claim. 

1.Jesus enters the synagogue on the Sabbath

[Luke 4:16] He went to Nazareth, where he had been brought up, and on the Sabbath day he went into the synagogue, as was his custom. And he stood up to read.

Jesus entered the synagogue to read the Scriptures, as he always did on the Sabbath. The Church of God claims that this is a scene of Jesus observing the Sabbath with the Jews. However, this is not a scene of observing the Sabbath, but of preaching the gospel to the Jews, and the evidence for this can be found in the following account.

[Luke 4:43~44] But He said to them, "I must preach the kingdom of God to the other cities also, for I was sent for this purpose." So He kept on preaching in the synagogues of Judea

2. Jesus' disciples enter the synagogue

[ Acts 17:2] As his custom was, Paul went into the synagogue, and on three Sabbath days he reasoned with them from the Scriptures,

Paul went into the synagogue on the Sabbath to discuss the Scriptures as he had always done, following the teachings of Jesus. The Church of God claims that this scene is of Paul observing the Sabbath with the Jews. However, this scene is not of Paul observing the Sabbath, but of Paul discussing the Scriptures in order to evangelize the Jews gathered in the synagogue on the Sabbath.

3.Find a place of prayer where people gather on the Sabbath.

[Acts 16:13~14] On the Sabbath we went outside the city gate to the river, where we expected to find a place of prayer. We sat down and began to speak to the women who had gathered there. One of those listening was a woman named Lydia, a dealer in purple cloth from the city of Thyatira, who was a worshiper of God. The Lord opened her heart to respond to Paul's message.

The Church of God claims that the above scene is of Paul observing the Sabbath, but it is a scene of Paul and his companions going to a place of prayer where Jews are gathered to evangelize them. Therefore, the Church of God's claim that Jesus and the apostles observed the Sabbath with the Jews is incorrect. While the Old Testament Sabbath was observed by the slaughter of a lamb without blemish or spot, the New Testament Sabbath is observed by the sacrifice of the saints who have been transformed by the Holy Spirit of God into bodies without blemish or spot. Therefore, the beautiful picture of the saints sacrificing for the sake of the gospel is the true Sabbath service.