Consecutive primes in short intervals

We obtain a lower bound for $$\#\{x/2< p_{n}\leq x:\ p_n \equiv\ldots\equiv p_{n+m}\equiv a\text{ (mod $q$)},\ p_{n+m} - p_{n}\leq y\},$$ where $p_{n}$ is the $n^{\text{th}}$ prime.