Trace of quotient spaces is usually seen wherever there is a study of a linear structure. In linear spaces, we use subspaces and their corresponding equivalence relation to define quotient spaces. With the same method, in this paper, we present two generalized structures of quotient space that are defined on quasilinear spaces. One of them is a quasilinear space and the other is a linear space. After that, we try to introduce norms on certain states of these spaces and examin some properties of them. We will also provide examples for better understanding throughout the process.