Jews in Synagogue

Sorry, but you are looking for simple answers to complex questions. Groups like the Ebionites surviving into the 5th century implies some continuing blurring of the Christian/Jewish dividing line. I have read of implied mingling of Christians in synagogues in Syria and Egypt a century later ... by inference not with proof. No search will give you anything more than "sound bytes" as to one person's evaluation of the sparse evidence. Read entire books on the general topic of the relationship between Christians and Jews in the first 5 centuries or so after Christ e.g.

• When Christians were Jews: The First generation by Paula Fredriksen
• After Jesus Before Christianity: A Historical Exploration of the First Two Centuries of Jesus Movements by Erin Vearncombe et. al.
• Mind the Gap: How the Jewish Writings between the Old and New Testament Help Us Understand Jesus by Matthais Henze
• Religion of the Apostles: Orthodox Christianity in the First Century by Stephen De Young
• Josephus, Paul, and the Fate of Early Christianity: History and Silence in the First Century by F. B. A. Asiedu

Each of these books can lead you to many similar books. This is merely a small sampling of the materials that are available.

History is not really my primary interest - DMB is likely a better source.  However, when I need references like this I turn to Oxford bibliographies Early Christianity - Classics - Oxford Bibliographies or other university provided bibliographies Early-Christianity-Resources-Bibliography.pdf (uwgb.edu) or even library guidance Find Books - HIST 3350: Early Christianities Research Guide - Research Guides at Sam Houston State University (shsulibraryguides.org)