  We present new generalized Cline's formula and Jacobson's lemma for the
g-Drazin inverse in a ring. These extend many known results, e.g., Chen and
Abdolyousefi (Generalized Jacobson's Lemma in a Banach algebra, Comm. Algebra,
{\bf 49}(2021), 3263--3272), Yan and Zeng (The generalized inverses of the
products of two elements in a ring, Turk. J. Math., {\bf 44}(2020),
1744--1756).
