Jordan-Wigner transformation and qubits with nontrivial exchange rule

Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Taking into account a model with local fermionic modes, formally only the "occupied" states $|1\rangle$ could be relevant for antisymmetry with respect to particles interchange, but "vacuum" state $|0\rangle$ is not. Introduction of exchange rule for such fermionic qubits indexed by some "positions" may look questionable due to general super-selection principle. However, a consistent algebraic construction of such "super-indexed" qubits is presented in this work. Considered method has some relation with construction of super-spaces, but it has some differences with standard definition of supersymmety sometimes used for generalizations of qubit model.