Summary: The main purpose of this paper is to present a systematic study of some families of multiple \(q\)-zeta functions and basic (or \(q\)-) \(L\)-series. In particular, by using the \(q\)-Volkenborn integration and uniform differentiation on \(\mathbb Z_p\), we construct \(p\)-adic \(q\)-zeta functions. These functions interpolate the \(q\)-Bernoulli numbers and polynomials. The values of \(p\)-adic \(q\)-zeta functions at negative integers are given explicitly. We also define new generating functions of \(q\)-Bernoulli numbers and polynomials. By using these functions, we prove the analytic continuation of some basic (or \(q\)-) \(L\)-series. These generating functions also interpolate Barnes’ type Changhee \(q\)-Bernoulli numbers with attached Dirichlet character. By applying the Mellin transformation, we obtain relations between Barnes’ type \(q\)-zeta function and new Barnes’ type Changhee \(q\)-Bernoulli numbers. Furthermore, we construct the Dirichlet type Changhee basic (or \(q\)-) \(L\)-functions.