Today we will look at the form आग्नेयस्य nGs from श्रीमद्भागवतम् Sb10.63.13.

ब्रह्मास्त्रस्य च ब्रह्मास्त्रं वायव्यस्य च पार्वतम् ।
आग्नेयस्य च पार्जन्यं नैजं पाशुपतस्य च ∥ १०-६३-१३ ∥

श्रीधर-स्वामि-टीका
प्रत्यस्त्राण्येवाह – ब्रह्मास्त्रस्येति । नैजं नारायणास्त्रम् ∥ १३ ∥

Gita Press translation “Against Brahmāstra He employed Brahmāstra; against Vāyavyāstra He employed the Pārvatāstra; against the fiery missile He employed the Pārjanyāstra and against the Pāśupatāstra He employed His own Nārāyaṇāstra (13).

The above verse has previously appeared in the following posts – पाशुपतस्य nGs and वायव्यस्य nGs

अग्निर्देवतास्‍येति = आग्नेयम् (अस्त्रम्) – (a missile) of which Agni is the presiding deity.
In the verses the विवक्षा is षष्ठी-एकवचनम्। Hence the form is आग्नेयस्य।

(1) अग्नि सुँ + ढक् । By 4-2-33 अग्नेर्ढक् – To denote something of the deity ‘अग्नि’, the तद्धित: affix ‘ढक्’ may be optionally applied following a syntactically related पदम् in which the सन्धिः operations have been performed, provided the पदम् ends in a nominative case affix and has a base denoting the name of the presiding deity ‘अग्नि’।
Note: The affix ‘ढक्’ prescribed by 4-2-33 अग्नेर्ढक् is अपवादः to the affix ‘अण्’ which would have applied (as per the सूत्रम् 4-2-24 सास्य देवता)।

(2) अग्नि सुँ + ढ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः। Note: The fact that the सूत्रम् 7-1-2 आयनेयीनीयियः फढखछघां प्रत्ययादीनाम्‌ (used in step 4) specifically prescribes the substitution ‘एय्’ in place of the letter ‘ढ्’ occurring in the beginning of an affix, obviously implies that the letter ‘ढ्’ in the beginning of an affix (such as ढक्) does not get the इत्-सञ्ज्ञा by 1-3-7 चुटू‌। Because, otherwise the letter ‘ढ्’ would be elided by 1-3-9 तस्य लोपः।

Note: ‘अग्नि सुँ + ढ’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 सुपो धातुप्रातिपदिकयोः to apply in the next step.

(3) अग्नि + ढ । By 2-4-71 सुपो धातुप्रातिपदिकयोः – A सुँप् affix takes a लुक् elision when it is a part of a धातुः or a प्रातिपदिकम्।

(4) अग्नि + एय् अ । By 7-1-2 आयनेयीनीयियः फढखछघां प्रत्ययादीनाम्‌ – The letters ‘फ्’, ‘ढ्’, ‘ख्’, ‘छ्’ and ‘घ्’ – when they occur at the beginning of a प्रत्यय: (affix) – are replaced respectively by ‘आयन्’, ‘एय्’, ‘ईन्’, ‘ईय्’ and ‘इय्’।
Note: As per the सूत्रम् 1-3-10 यथासंख्यमनुदेशः समानाम्, the substitutions take place respectively.

Note: The affix ढक् is a कित् (has the letter ‘क्’ as a इत्) and this allows 7-2-118 to apply in the next step.

(5) आग्नि + एय । By 7-2-118 किति च – The first vowel among the vowels of a अङ्गम् which is followed by a तद्धित: affix (ref. 4-1-76 तद्धिताः) which is a कित् (has the letter ‘क्’ as a इत्) takes the वृद्धि: (ref. 1-1-1 वृद्धिरादैच्) substitute.

Note: The अङ्गम् ‘आग्नि’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(6) आग्न् + एय । By 6-4-148 यस्येति च – When the letter ‘ई’ or a ‘तद्धित’ affix follows, the (ending) इ-वर्ण: (letter ‘इ’ or ‘ई’) or the (ending) अवर्ण: (letter ‘अ’ or ‘आ’) of the अङ्गम् with the भ-सञ्ज्ञा takes elision (लोपः)।

= आग्नेय । Note: The प्रातिपदिकम् ‘आग्नेय’ is an adjective. In the present example, it is qualifying the neuter noun अस्त्रम्। Hence, it declines like वन-शब्दः।