Summary: For any nonempty closed set \(E\) in the unit circle, any positive number \(\lambda\) and any real number \(\mu\), \((0\leq \mu \leq \lambda)\), we construct a meromorphic function \(f(z)\) of order \(\lambda\) in the unit disc, which takes the set \(\{L(\theta)|\theta\in E\}\) as its Borel radii set and the set \(\{L(\theta)|\theta \not\in E\}\) as its non-Julia radii set. The order of its counting function \(N(r,f)\) is \(\mu\).