  We study a general ansatz for an odd supersymmetric version of the Kronecker
elliptic function, which satisfies the genus one Fay identity. The obtained
result is used for construction of the odd supersymmetric analogue for the
classical and quantum elliptic $R$-matrices. They are shown to satisfy the
classical Yang-Baxter equation and the associative Yang-Baxter equation. The
quantum Yang-Baxter is discussed as well. It acquires additional term in the
case of supersymmetric $R$-matrices.
