Summary

it's clear from the literature that OA articles are cited more than articles that are only accessible behind a paywall. There are very many studies documenting this. There are very few studies that found OA articles aren't cited more, and none have ever found that they're cited less. There are some theories that other factors cause the OA citation advantage, which includes number of others, authors only making their higher quality papers OA, and early dissemination of preprints.

A Sample of Research that found a Citation Advantage

Lawrence, S. Free online availability substantially increases a paper's impact. Nature, 411(May 2001), 521-521. https://www.nature.com/articles/35079151.pdf. MF

Appears to be the earliest study of open access citation advantage. Lawrence studied 119,924 computer science articles and found a 157% increase (~2.5 times more likely) in the mean number of citations of OA articles over non-OA.

Brody, T. D. Evaluating research impact through open access to scholarly communications [PhD. Thesis, Philosophy]. University of Southampton, School of Electronics and Computer Science. 2006.http://eprints.soton.ac.uk/263313/. MF

Articles self-archived by authors receive between 50-250% more citations. Rapid pre-printing on the Web has dramatically reduced the peak citation rate from over a year to virtually instantaneously. In addition to discussing citation impact, the thesis describes a new web metric, download impact.

Antelman, K. Do open-access articles have a greater research impact? College & Research Libraries, 65 (2004), no. 5, 372-382. https://crl.acrl.org/index.php/crl/article/view/15683. MF

 Web of Science citation rates are enhanced for OA articles over non-OA articles by 91% for mathematics, 51% for electrical and electronic engineering, 86% for political science) and 45% for philosophy.

Norris, M., Oppenheim, C., & Rowland, F. The Citation advantage of open-access articles. Journal of the American Society for Information Science and Technology, 59 (2008), no. 12, 1963-1972. https://onlinelibrary.wiley.com/doi/abs/10.1002/asi.20898. MF

A study of four subject areas (ecology, applied mathematics, sociology, and economics) showed an average of 57% more citations for journal articles that have an open access version vs. those that are exclusively toll access (subscription-based). 

Eysenbach, G. Citation advantage of open access articles. PLoS Biology, 4 (2006), no. 5, 692-698.https://pubmed.ncbi.nlm.nih.gov/16683865/. MF

A study of open access vs. non-open access articles in the same journal, Proceedings of the National Academy of Science. Open access articles twice as likely to be cited and were more heavily cited than non-OA articles.  Research was controlled for confounding variables including: number of authors, authors' lifetime publication count and impact, submission track, country of corresponding author, funding organization, and discipline.

Davis, P. M. Author-choice open-access publishing in the biological and medical literature: a citation analysis. Journal of the American Society for Information Science and Technology, 60 (2009), no. 1, 3-8. https://onlinelibrary-wiley-com.proxy-bc.researchport.umd.edu/doi/epdf/10.1002/asi.20965. MF

A study of 11 biological and medical journals from 2003-2007 that publish both open access and subscription access articles (author-choice model). The study indicates an average citation advantage for open access articles of 17%. Controlled for number of authors, number of references, length in pages, whether the article was a review, and whether the author was located in the U.S.

Evans, J. A., & Reimer, J. Open access and global participation in science. Science, 323 (2009), no. 5917, 1025-1025. https://www.science.org/lookup/doi/10.1126/science.1154562. MF

Although showing a more modest effect for open access advantage (~8% on average), this study clearly demonstrates that open access articles are much more likely to be cited in poorer countries. D