We investigate the spectral properties of a class of Sierpinski-type self-affine measures defined by \( \mu _{M,D}(\cdot ) = p^{-1} \sum _{d \in D} \mu _{M,D}(M(\cdot ) - d), \) where \( p \) is a prime number, \( M = \begin{bmatrix} \rho _1^{-1} & c \\ 0 & \rho _2^{-1} \end{bmatrix} \) is a real upper triangular expanding matrix, and \( D = \{d_0, d_1, \cdots , d_{p-1}\} \subset \mathbb {Z}^2 \) satisfying \( \mathcal {Z}(\widehat{\delta }_{D}) = \cup _{j=1}^{p-1} ( \frac{j \varvec{a}}{p} + \mathbb {Z}^2 ) \) for some \( \varvec{a} \in \mathcal {E}_{p}= \{ (i_1, i_2)^* : i_1, i_2 \in [1, p-1] \cap \mathbb {Z} \} \) . Here \( \mathcal {Z}(\widehat{\delta }_{D}) \) denotes the set of zeros of \( \widehat{\delta }_{D} \) with \( \delta _{D} = \frac{1}{\# D} \sum _{d \in D} \delta _d \) . When \(\rho _1 = \rho _2\) , we derive necessary and sufficient conditions for \(\mu _{M,D}\) to both: (i) possess an infinite orthogonal set of exponential functions, and (ii) be a spectral measure. When no infinite orthogonal exponential system exists in \(L^{2}(\mu _{M,D})\) , we quantify the maximum number of orthogonal exponentials and provide precise estimates. For \(\rho _1 \ne \rho _2\) , with restricted digit sets D, we obtain a necessary and sufficient condition for \(\mu _{M,D}\) to be a spectral measure.
