Alkac, GokhanMesta, MuratUnal, Gonul2025-12-052025-12-0520252470-00102470-002910.1103/1ws1-x8z32-s2.0-105020864993https://doi.org/10.1103/1ws1-x8z3https://hdl.handle.net/20.500.14411/10964We construct a consistent three-dimensional Einstein-Gauss-Bonnet theory as a vector-tensor theory within the generalized Proca class by employing a regularization procedure based on the Weyl geometry, which was introduced recently by Charmousis, Fernandes, and Hassaine [Phys. Rev. D 111, 124008 (2025).]. We then obtain an asymptotically Anti-de Sitter (AdS3), static, and circularly symmetric black hole solution with primary Proca hair. Afterward, we investigate the effect of the scalar-tensor GaussBonnet coupling constructed previously by different regularization schemes. We further generalize these solutions by incorporating an electric charge. As special cases, we find a regular black hole solution in addition to charged and uncharged stealth Banados-Teitelboim-Zanelli black hole solutions.eninfo:eu-repo/semantics/openAccessArticle