In this paper, we establish Schr\"{ o}dinger maximal estimates associated with the finite type phases \begin{ equation*} \phi(\xi_1,\xi_2):=\xi^m_1+\xi^m_2,\;(\xi_1,\xi_2)\in [0,1]^2, \end{ equation*} where $m \geq 4$ is an even number. Following [12], we prove an $L^2$ fractal restriction estimate associated with the surfaces \begin{ equation*} F^2_m:=\{ (\xi_1,\xi_2,\phi(\xi_1,\xi_2)):\;(\xi_1,\xi_2)\in [0,1]^2\} \end{ equation*} as the main result, which also gives results on the average Fourier decay of fractal measures associated with these surfaces. The key ingredients of the proof include the rescaling technique from [16], Bourgain-Demeter's $\ell^2$ decoupling inequality, the reduction of dimension arguments from [17] and induction on scales.
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