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One of the most crucial parts of applying a regularization method to solve an ill-posed problem is choosing a regularization parameter to obtain an optimal order error estimate. In this paper, we consider the finite dimensional realization of the parameter choice strategy proposed in [C. Mekoth, S. George and P. Jidesh. Fractional Tikhonov regularization method in Hilbert scales. Appl. Math. Comput.(2021), 392: 125701, 26 DOI:10.1016/j.amc.2020.125701] for Fractional Tikhonov regularization method for linear ill-posed operator equations in the setting of Hilbert scales.