Some suggested subject headings (please note the use of the search term "periodicals" for both journals and newspapers and the term "newspapers" for that format only) :
Russian periodicals -- Bibliography
Soviet Union -- History -- Bibliography
Soviet Union -- Periodicals -- Indexes
Russian newspapers -- Bibliography
Soviet newspapers -- Bibliography
Russian newspapers -- Soviet Union -- Bibliography
Russian newspapers -- Indexes -- Periodicals
Soviet newspapers -- Bibliography
Soviet periodicals -- Bibliography.
Turkmenistan -- Periodicals -- Indexes -- Periodicals
Ukrainian newspapers -- Bibliography.
Ukrainian newspapers -- Indexes
You can also play around with other combinations of subject terms. For this type of search, select “Subject → contains”, not “Subject → exact phrase” and combine terms such as: "Russia", "Soviet", "journals", "periodicals", "newspapers", "indexes", "bibliography", etc.
Search in the digital catalogs of journals and newspapers on the websites of libraries in the region, such as:
Newspapers and Serial Publications at the Russian State Library
Newspapers and Journals at the Russian National Library (digital copies of many newspaper editions available online)
Periodicals and continuing publications in Russian, Ukrainian, and Belarusian (except newspapers)
Periodicals and continuing publications in foreign (European) languages (except newspapers)
Catalog of Periodicals at the Russian State Public Historical Library (organized by place of publication, providing article-level information)
Domestic Periodicals in the Fond of the Presidential Library of Russia (digital copies available)
Periodical publications at the Saint-Petersburg State Theater Library
Digital Archive of National Periodicals of Uzbekistan
General strategy: visit the website of the library that might be of interest to you (related to your research’s geographical/thematic focus) and find the digital catalog, which most libraries have developed. Most libraries’ digital catalogs allow users to search/browse by material type, either through separate sub-collections/catalogs or via faceted navigation. On the websites of some local libraries, sometimes you can find very niche local sources.
If the journals and newspapers you’re interested in happen to be included in the East View database, you could try full-text article searches in the East View database.
Bibliographic Resources
Letopis' periodicheskikh izdanii SSSR: trudy, uchenye zapiski, sborniki i drugie prodolzhaiushchiesia izdaniia. Moscow: Vsesoiuznaia Knizhnaia Palata, 1951-1970. FOLLOWED BY: Letopisʹ periodicheskikh i prodolzhaiushchikhsia izdanii: Novye, pereimenovannye i prekrashchennye izdaniem zhurnaly i gazety. Moscow: Vsesoiuznaia knizhnaia palata, 1971-1996.
Periodicheskai︠a︡ pechatʹ SSSR, 1917-1949; bibliograficheskiĭ ukazatelʹ. 9 vols. Moscow: Vsesoi︠u︡znai︠a︡ knizhnai︠a︡ palata, 1955.
Russkaia periodicheskaia pechatʹ: ukazateli soderzhaniia, 1728-1995. Eds. V. N. Nitkina and N. K. Lelikova. St. Petersburg: Izdatel’stvo Rossiiskoi natsional’noi biblioteki, 1998.
[Il’inskii, Leonid Konstantinovich. Spisok povremmennykh [sic] izdanii za 1917 g. Ed. and intro. David R. Jones. White Plains, NY: Kraus International Publications, 1986.
Ukazatel' sovetskoi periodicheskoi pechati: 1208 nazvanii sovetskikh gazet i zhurnalov. Munich: Institut für Erforschung der Geschichte und Kultur der UdSSR, 1954.
Universiteit van Amsterdam. Oost-Europa Instituut. The Soviet World, 1948-[1989] :a Bibliography of Articles from the Soviet and Western Press. Inter Documentation Company, 1991.. Microforms, Harvard University Lamont Library, Microfiche W 4340.
Note: The guide to this collection is online at Brill. It can be found as a downloadable PDF at the bottom of the page on the site of the collection on Brill.
Russian periodicals bibliographies on HathiTrust (You can identify bibliographic resources here, and then check if they are in the records of HOLLIS)
Digitized Letopisi zhurnal’nykh statei (1926-1990) and Letopisi gazetnykh statei (1936-1987). The database is not word-searchable but one can consult the indexes at the end of each edition to ease the search process.
Additional Sources
Index to Russian and Ukrainian periodicals available on microfilm from the Library of Congress Photoduplication Service. Ed. John P. Balys. Washington, D. C.: Library of Congress, Photoduplication Service, 1968.
Half a century of Soviet serials, 1917-1968 : a bibliography and union list of serials published in the USSR. Ed. Rudolf Smits. 2 vols. Washington, DC: Library of Congress, 1968.
Note: this resource is dated but can be useful for browsing.
The Current Digest of the Russian Press. Minneapolis: East View Information Services, 1949-2020. (Formerly The Current Digest of the Soviet Press (1949-1991) and The Current Digest of the Post-Soviet Press (1992-2010). The link above redirects to all issues, 1949-present.)
Annual index to the Current digest of the Soviet press. Vol. 28-vol. 43. Columbus, Ohio: American Association for the Advancement of Slavic Studies, 1976-1992.
Central Asian Review, London, Published by the Central Asian Research Centre in association with the Soviet Affairs Study Group, St. Antony's College, Oxford (1953-1968)
Digital Handbook for Research on Soviet History contains information about open-access Soviet periodical resources. You can browse these resources via this link.
Letopisʹ zhurnalʹnykh statei. Moscow: Izdatel’stvo Vsesoiuznoi knizhnoi palaty, 1926- A searchable digital version of issues 1926-1990 available to Harvard uers as: Nauchno-izdatelʹskiĭ proekt "Ėlektronnai︠a︡ kollekt︠s︡ii︠a︡ Letopiseĭ RKP za 100 let (1917-2017 gg.)
Katalog otechestvennykh zhurnalov na russkom iazyke za 1917-1977 gg., khraniashchikhsia v fondakh GPIB : v 4-kh vyp. Moscow: Ministerstvo kulʹtury RSFSR and Gosudarstvennaia publichnaia istoricheskaia biblioteka, 1981.
Gazety SSSR. 1917-1960. Bibliograficheskii spravochnik. Ed. G. L. Episkoposov. 5 vols. Moscow: Vsesoiuznaia knizhnaia palata, Gosudarstvennaia biblioteka SSSR im. V. I. Lenina, and Gosudarstvennaia publichnaia biblioteka im. M. E. Saltykova-Shchedrina, 1970-1984.
Kuznetsov, I. V. Gazetnyi mir Sovetskogo Soiuza, 1917-1970 gg. Moscow: Izdatel’stvo Moskovskovo universiteta, 1972-1976.
Letopis’ gazetnykh statei. Moscow: Vsesoiuznaia knizhnaia palata, 1936-
Note that the 1936-1987 issues are available online through HOLLIS as Nauchno-izdatelʹskiĭ proekt "Ėlektronnai︠a︡ kollekt︠s︡ii︠a︡ Letopiseĭ RKP za 100 let (1917-2017 gg.)." The rest must be found in print.
Akopian, T. V. et al. Odnodnevnye gazety SSSR 1917-1983: One-Day Newspapers, 1917-1983. New York: Norman Ross Pub.; Moscow: National Library of Russia, 1993. Microform, Harvard University.
Note this review of this collection by Jeffrey Brooks, which includes some information about it and about other resources related to it.
Anti-Soviet Newspapers, 1918-1924. Leiden: IDC Publishers, 2004. Microfilm, Harvard University,
Gazety pervykh let sovetskoi vlasti, 1917-1922 : svodnyi bibliograficheskii katalog. 4 vols. Eds. I. V. Morozova and O. N. Nizhneva. Moscow: Gosudarstvennaia biblioteka SSSR im. V. I. Lenina, 1990.
The GULAG Press, 1920-1937. Leiden: IDC Publishers, 2000. Microfiche, Harvard University, Microfiche W 6041.
Note: This collection includes 134 titles containing news bulletins, posters, literary journals, albums and booklets. It has several Turkic-language papers from the USSR).
Newspapers from the Era of the Russian Revolution and the Russian Civil War 1901-1922. New York: UMI SERIALS, 2003. Microfilm, Harvard University, Film NC 2484.
Newspapers from the Russian Revolutionary Era: Temporary Guide to the Microfilm Collection. Woodbridge, CT: Research Publications, 1983-1988. Microfilm, Harvard University, Z2495. N39.
Newspapers of the October Revolution: January 3, 1917 through December 31, 1917. Washington, D.C.: Library oF Congress Photoduplication Service, 2005.
Sovetskaia satiricheskaia pechat’: 1917-1963. Eds. S. I. Stykalin and I. K. Kremenskaia. Moscow: Gosudarstvennoie izdatel’stvo politicheskoi literatury, 1963.
Digital copy of Gazety SSSR. 1917-1960. Bibliograficheskii spravochnik. (word-searchable)
Digital copy of Akopian, T. V. et al. Odnodnevnye gazety SSSR 1917-1983: One-Day Newspapers, 1917-1983.