Let \( q \) be an integer greater than or equal to 2, and let \( S_q(n) \) denote the sum of digits of \( n \) in base \( q \). For

\[
\alpha = [0; \overline{1,m}], \quad m \geq 2,
\]

let \( S_\alpha(n) \) denote the sum of digits in the Ostrowski \( \alpha \)-representation of \( n \). Let \( m_1, m_2 \geq 2 \) be integers with

\[
\gcd(q-1, m_1) = \gcd(m_2) = 1.
\]

We prove that there exists \( \delta > 0 \) such that for all integers \( r_1, r_2 \),

\[
\big|\{0 \leq n < N : S_q(n) \equiv r_1 \pmod{m_1},\ S_\alpha(n) \equiv r_2 \pmod{m_2}\}\big| = \frac{N}{m_1 m_2} + O(N^{1-\delta}). \]

The asymptotic relation implied by this equality was proved by Coquet, Rhin & Toffin and the equality was proved for the case \( \alpha = [\overline{1}] \) by Spiegelhofer.