Yes, There Were Jews in Judea and Samaria During Mandate Time

This is a table of land holding in 1922 and 1932 by the Jewish Agency with population figure as per official Mandate authorities records:

Seven Jews in 1922 and down to 4 in 1932 (that's after the infamous 1929 riots).

And this is a pacelization map of an area east of Petah Tikva, called Ramat Tikvah, which was purchased by Jews from Arabs in Rantis also during the Mandate era, in 1934, and it lies just east of the Green Line and the current boundary of the new security barrier, not far the Bet Aryeh: