Palsy of right genioglossus causes:

Genioglossus muscle moves the tongue anterior, inferior and medial (AIM). Bilateral contraction of genioglossus help in protrusion and depression of tongue in midline, since the vector of medial pull is balanced and cancelled. Palsy of right genioglossus muscle deviates the tongue to the right side, due to unopposed medial  pull of the left genioglossus.