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I am using a 8 bit Sbox having 16 entries with a lookup table of 4x4 in cryptographic algorithm. Sbox is constructed on subgroup of galois field 2^8. I want to calculate number of quadratic equations used to describe this Sbox over GF(2) so I can calculate resistance of algorithm against algebraic attacks.Since AES Sbox can be described by 23 quadratic equations and my Sbox is also 8 bit but its size is small having 16 entries only. So kindly if anyone can tell by how many quadratic equations my Sbox can be represented over GF(2)?

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You cannot, without fully specifying the Sbox table. The equations are determined by something like a grobner basis algorithm or some other means which require input of the Sbox specification.

See https://eprint.iacr.org/2017/007.pdf

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