Factorization Patterns for Ideals

Question

Let $K/\mathbb{Q}$ be a Galois Number field. Let $p$ be an unramified rational prime. In this extension, for any $P,Q | p\mathcal{O}_K$ then the relative degrees $f(P) := [\mathcal{O}_K/P : \mathbb{Z}/p\mathbb{Z}]$ satisfy $f(P) = f(Q)$. The Chebotarev density theorem gives statistical information on the size of sets of rational primes $p$ such that the primes lying above $p$ have a specific Frobenius conjugacy class. On the other hand, it does not provide information on how many rational primes in Galois extensions have a fixed $f(P)$ (aside from primes that split i.e. $f(P) = 1$, which will have trivial conjugacy class). Are there any general results about the statistics of primes with specific values $f(P)$? In the Abelian case? I would appreciate any references about this.