Let $\mathbb{P}_{a, q}$ denote the set of primes congruent to $a$ modulo $q$. Are there any estimates for the number of $3$-Arithmetic Progressions in the set $\mathbb{P}_{a, q}\cap [1, X]$, where $(a, q) = 1$? For $q$ at most a constant, such an estimate can be given thanks to Green. One can take a slightly better $q$ thanks to the work of Helfgott and Roton. In both works, they deal with a much more general setting. Can one gain in how large of a modulus $q$ is admissible if one restricts specifically to $\mathbb{P}_{a, q}\cap [1, X]$?