To my knowledge there is no specific journal devoted exactly to ancient Semitic languages and their comparison. But there are more general journals where you can find papers devote to one or another Semitic language, including of course Hebrew. Such as:

Journal of Semitic Studies, Manchester, UK;

Semitica, Paris;

But you may also find interesting material in more general journals devoted to Oriental studies, such as:

Journal of American Oriental Society;

Journal of Near Eastern Studies, Chicago;

Zeitschrift der Deutschen Morgenländischen Gesellschaft;

and many others.

On the other hand every ten years or so, there would be published a general monograph on Semitic languages that would show the progress of studies in Semitic linguistics with chapters written by leading experts on all the special languages, and the comparative research: Such as:

The major languages of South Asia, the Middle East and Africa, edited by Bernard Comrie, (The Major Languages), London: Routledge, 1990;

The Semitic languages, edited by Robert Hetzron, (Routledge Language Family Descriptions), London: Routledge, 1997;

Bennett, Patrick R., Comparative Semitic linguistics: a manual, Winona Lake, IN: Eisenbrauns, 1998;

Lipinski, Edward, Semitic languages: outline of a comparative grammar, second edition, (Orientalia Lovaniensia Analecta, 80), Leuven: Uitgeverij Peeters en Departement Oosterse Studies, 2001 (1997),

Semitic Linguistics: The State of the Art at the Turn of the Twenty-First Century, edited by Shlomo Izre’el, (Israel Oriental Studies, 20), Winona Lake, IN: Eisenbrauns, 2002;

Semitic languages in contact, edited by Aaron Michael Butts, Leiden ; Brill, 2015.

I hope this list will help you to start your studies,

______ Witold Witakowski, PhD Associate Professor of Semitic Languages, rtd Uppsala University, Sweden

To my own understanding, you may not see any journal specifically for the ancient semitic language and comparison. But you can see other journals that can assist carryout your research in such area