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