Tabla is a musical instrument composed of two drums, the Bayan (left on picture) and the Dayan (right on picture).
A unique feature of the tabla is the tuning [black] paste called the gab, applied to the center of the dayan and off-center on the bayan. Typically when a membrane stretched over a resonating body is struck there is no clear sense of pitch because the sound produced is rich in inharmonic overtones. The gab when properly applied causes these inharmonic partials to be damped giving the dayan a clear sense of pitch when struck correctly.
(cited from this webpage; see also this Nature paper).
This explains why the black paste "gab" is added to the drum skins, however, it does not give any reasons why the Bayan's gab is off-centered on the Bayan. As it is always the case for Bayan and never for Dayan, I expect that the drum designers do it by purpose.
Q: Is there any physical reason to have the black load to be off-set on the Bayan? Theoretically, what would be the effect of this off-setting on the sound, if any?
Note that the skin of the largest one (Bayan) is far less stretched than the smallest one (Dayan) and the playing techniques are very different (for instance, see here for the largest drum and here for the smallest one).