The y of a Patronymic affix, preceded by a consonant, is elided before a taddhita when it does not begin with an ā,
Thus गर्गाणां समूहः = गार्गकम् from गार्ग्य, वात्सकम् from वात्स्य 4.2.37 — 4.2.40. Why do we say 'a Patronymic य'? Observe सांकाश्यकः, काम्पिल्यकः 4.2.80.
The repetition of the word Taddhita indicates that the elision takes place some-times of the non-patronymic य also, as सामी इष्टिः ॥
Why do we say 'not beginning with a long आ'? Observe गार्ग्यायणः, वात्स्यायनः ॥ The य should be preceded by a consonant, otherwise we have कारिकेयस्यापत्यं = कारिकेयिः ॥ Why do we say 'when followed by a Taddhita affix'? Observe गार्ग्ययोः, वात्स्ययोः (before the Genitive and Locative dual affixes).,