I have been thinking about what we mean when we say "Jewish Christian" in New Testament terms. Craig Hill makes offers the following suggestion.
"It would be possible to call the members of the Jerusalem church 'Jewish Christians' and mean by it only that these were Christian believers whose ethnic identity (to use modern category) was Jewish. That would be little different from saying that someone is an Irish athlete or an African American singer. These designations tell us something specific about the person but nothing particular about the form of athletics or the type of singing. Few people speak of Jewish Christianity in this sense. Instead, the qualifier 'Jewish' is substantive: a Jewish Christian is one whose self-understanding, beliefs, and practices are substantially both Jewish and Christian."
Craig C. Hill, "the Jerusalem Church," in Jewish Christianity Reconsidered: Rethinking Ancient Groups and Texts, ed. Matt Jackson-McCabe (Minneapolis: Fortress, 2007), 45.