The affix tasi comes optionally after a word ending in the Genitive 6th-Case when the sense is that of a party-name or function.,
Taking sides with one faction or another is called व्याश्रयः ॥ Thus देवा अर्जुनस्य पक्षेऽभवन् = देवा अर्जुनतोऽभवन् ॥ 'The Devas became Arjunites'. So also आदित्याः कर्णतोऽभवन्. \The Adityas became Karnaites\.
Why do we say \when it denotes a Party-name\? Observe, वृक्षस्य शाखा \the branch of the tree\.,