New estimates for the exceptional set of the sum of two primes from an arithmetic progression

The paper studies the question of representing numbers as the sum of two primes from an arithmetic progression, that is, the binary Goldbach problem, when primes are taken from an arithmetic progression. New estimates are proved for the number of even natural numbers that are (possibly) not representable as a sum of two primes from an arithmetic progression and for a number representing a given natural number, as a sum of two primes from an arithmetic progression.