The main objective of this work is to investigate a novel class of polynomials, called the ∆ h -Sheffer polynomials and to explore their various properties.The generating function, explicit representations, quasi-monomiality, and certain novel identities involving ∆ h -Sheffer polynomials are obtained.Also, the ∆ h -Sheffer polynomials are explored via determinant representation.Further, the ∆ h Gould-Hopper-Sheffer polynomials are introduced with the help of ∆ h -Sheffer and ∆ h Gould-Hopper polynomials.Certain fascinating results, such as the generating function, determinant form, multiplicative, and derivative operators and many more results for these hybrid form of the ∆ h -Sheffer polynomials are also obtained.Certain examples are considered as the special cases of ∆ h Gould-Hopper-Sheffer polynomials.