Suppose that \(\varphi=(\varphi_n)_{n=0}^{\infty}\) is a sequence of real numbers. Then the series \(\sum_{n=0}^{\infty}a_n\) is said to be indexed almost absolute convoluted Nörlund-summable \(\varphi\)-\(|N, p, q; m|_k\) of order \(k\geq 1\) if the series \[ \sum_{n=1}^{\infty}|\varphi_n(t_{n, m}^{p, q}-t_{n-1, m}^{p, q})|^k \] is uniformly convergent with respect to \(m\), where \(t_{n, m}^{p, q}\) is defined by \begin{align*} t_{n, m}^{p, q}&=\frac{1}{(p*q)_n}\sum_{\nu=0}^{n}p_{n-\nu}q_\nu s_{\nu, m},\\ s_{n, m}&=\frac{1}{n+1}\sum_{\nu=n}^{n+m}s_\nu,\ \text{ and } \\ (p*q)_n&=\sum_{\nu=0}^{n}p_{n-\nu}q_\nu. \end{align*} Let \(\Phi_n(x)\) be an orthonormal system. In this paper, the authors obtain some sufficient conditions under which the orthonormal series \(\sum_{n=0}^{\infty}a_n\Phi_n(x)\) is almost everywhere \(\varphi\)-\(|N, p, q; m|_k\) summable.