The affix ḍhak comes after the words 1. vikarṇa and 2. kuṣīta when they mean the descendants of kāśyapa,
Thus वैकर्णेयः and कौषीतकेयः = काश्यपः; otherwise we have वैकर्णिः and कौषीतकिः formed by 4.1.95.,
विकर्ण-कुषीतकात् काष्यपे
Adhyāya 4 · Pāda 1 · Rule 124