Around q-Appell polynomial sequences

First we show that the quadratic decomposition of the Appell polynomials with respect to the q-divided difference operator is supplied by two other Appell sequences with respect to a new operator Mq;q-eq;q?, where ? represents a complex parameter different from any negative even integer number. While seeking all the orthogonal polynomial sequences invariant under the action of MÖq;q-e/2q;q?2 (the MÖq;q-e/2q;q?2 -Appell), only the Wall q-polynomials with parameter q ?/2+1 are achieved, up to a linear transformation. This brings a new characterization of these polynomial sequences.