<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>AdS</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> black holes with primary Proca hair from a regularized

We 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 [.]. We then obtain an asymptotically Anti-de Sitter ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mtext>AdS</a:mtext> <a:mn>3</a:mn> </a:msub> </a:math> ), static, and circularly symmetric black hole solution with primary Proca hair. Afterward, we investigate the effect of the scalar-tensor Gauss-Bonnet 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.