  The gamma-ray observation of dwarf spheroidal satellites (dSphs) is an ideal
approach for probing the dark matter (DM) annihilation signature. The latest
Fermi-LAT dSph searches have set stringent constraints on the velocity
independent annihilation cross section in the small DM mass range, which gives
very strong constraints on the scenario to explain the the AMS-02 positron
excess by DM annihilation. However, the dSph constraints would change in the
velocity dependent annihilation scenarios, because the velocity dispersion in
the dSphs varies from that in the Milky Way. In this work, we use a likelihood
map method to set constraints on the velocity dependent annihilation cross
section from the Fermi-LAT observation of six dSphs. We consider three typical
forms of the annihilation cross section, i.e. p-wave annihilation, Sommerfeld
enhancement, and Breit-Wigner resonance. For the p-wave annihilation and
Sommerfeld-enhancement, the dSph limits would become much weaker and stronger
compared with those for the velocity independent annihilation, respectively.
For the Breit-Wigner annihilation, the dSph limits would vary depending on the
model parameters. We show that the scenario to explain the AMS-02 positron
excess by DM annihilation is still viable in the velocity dependent cases.
