Most of the existing constitutive models often relay on parameters that lack actual physical significance to account for the structure of soil, while neglecting the influence of structural yield stress. To address this gap, a structure parameter ξ incoporating the relationship between the shear strength of undistributed and remolded soils is proposed. Within the framework of critical state theory, a modified Cam-clay model is developed. This model employs Caputo-type fractional differential to describe the characteristics of soil plastic flow direction in the soil and the non-orthogonality of the yield surface. Consequently, a fractional constitutive model considering the structural effects in clay is established. The model is validated by Wenzhou clay and Osaka clay. When the stress of the soil is less than the structural yield stress, the structural parameter ξ>1, indicating that the mechanical properties of the soil are significantly affected by the structural properties. Conversely, when the stress of the clay is larger than the structure yield stress, the structural parameter ξ=1, and the structural influence disappears, allowing the model to reduce to a conventional fractional constitutive model. The prediction results of Wenzhou clay show that, when the confining pressure is 0,0, and 200 kPa, the fractional constitutive model considering the structural influence reduces the maximum prediction error by 27.6%, 13.05% and 1.8%, respectively, compared to the model ignoring the structural influence, with an average maximum prediction error of 4.92%. Further validation using prediction results of Osaka clay demonstrates that the model better predicts the mechanical and deformation characteristics of structural clay, exhibiting good applicability and reliability.