Today we will look at the forms दैत्यान् mAp, आदित्याः mNp from श्रीमद्-वाल्मीकि-रामायणम् 3.14.15.

पुत्रांस्त्रैलोक्यभर्तॄन्वै जनयिष्यथ मत्समान् । अदितिस्तन्मना राम दितिश्च दनुरेव च ।। ३-१४-१३ ।।
कालका च महाबाहो शेषास्त्वमनसोऽभवन् । अदित्यां जज्ञिरे देवास्त्रयस्त्रिंशदरिन्दम ।। ३-१४-१४ ।।
आदित्या वसवो रुद्रा अश्विनौ च परन्तप । दितिस्त्वजनयत्पुत्रान्दैत्यांस्तात यशस्विनः ।। ३-१४-१५ ।।

Gita Press translation – ‘You will give birth to sons like me, masters of the three worlds.’ O Rāma of mighty arms – Aditi, Diti, Danu and Kālakā were attentive, the rest were indifferent. “Of Aditi thirty-three gods were born, O vanquisher of foes – the (twelve) Ādityas, the (eight) Vasus, the (eleven) Rudras and the two Aświns, O tormentor of foes! Diti for her part gave birth to the famous Daityas (demons), O dear one! (13-15).”

The above verses have previously appeared in the following post – जनयिष्यथ 2Ap-लृँट्

दितेरपत्यम् (पुमान्) = दैत्यः – a (male) descendant of Diti
In the verses the विवक्षा is द्वितीया-बहुवचनम्, hence the form used is दैत्यान्।

(1) दिति ङस् + ण्य । By 4-1-85 दित्यदित्यादित्यपत्युत्तरपदाण्ण्यः – The affix ‘ण्य’ is authorized for all rules down prior to the सूत्रम् 4-4-2 तेन दीव्यति खनति जयति जितम्, provided it is applied to a पदम् derived from a प्रातिपदिकम् which is either ‘दिति’, ’अदिति’, ’आदित्य’ or a compound which has ‘पति’ as its latter member.
Note: The affix ‘ण्य’ prescribed by this सूत्रम् is a अपवादः to the affix ‘अण्’ prescribed by the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण्।
As per the सूत्रम् 4-1-92 तस्यापत्यम् – Following a syntactically related पदम् in which the सन्धिः operations have been performed and which ends in a sixth case affix the तद्धिता: affixes already prescribed (by the prior rules 4-1-83 प्राग्दीव्यतोऽण् etc), as well as those that are going to be prescribed (by the following rules 4-1-95 अत इञ् etc), may be optionally applied to denote the sense of अपत्यम् (descendant.)

(2) दिति ङस् + य । अनुबन्ध-लोपः by 1-3-7 चुटू, 1-3-9 तस्य लोपः।

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

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

Note: The affix ‘ण्य’ is a णित् (has the letter ‘ण्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) दैति + य । By 7-2-117 तद्धितेष्वचामादेः – The first vowel among the vowels of a अङ्गम् which is followed by a तद्धित: affix (ref. 4-1-76 तद्धिताः) which is either a ञित् (has the letter ‘ञ्’ as a इत्) or a णित् (has the letter ‘ण्’ as a इत्) takes the वृद्धि: (ref. 1-1-1 वृद्धिरादैच्) substitute.

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

(5) दैत् + य । 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)।

= दैत्य । The प्रातिपदिकम् ‘दैत्य’ declines like राम-शब्दः।

(6) दैत्य + शस् । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्‌।

(7) दैत्य + अस् । अनुबन्ध-लोपः by 1-3-8 लशक्वतद्धिते and 1-3-9 तस्य लोपः। 1-3-4 न विभक्तौ तुस्माः prevents the ending letter ‘स्’ of ‘शस्’ from getting the इत्-सञ्ज्ञा ।

(8) दैत्यास् । By 6-1-102 प्रथमयोः पूर्वसवर्णः – When a अक् letter is followed by a vowel (अच्) of the first (nominative) or second (accusative) case then for the two of them (अक् + अच्) there is a single substitute which is the elongated form of the first member (the अक् letter.)

(9) दैत्यान् । By 6-1-103 तस्माच्छसो नः पुंसि – In the masculine gender, when the letter ‘स्’ of the affix ‘शस्’ follows a vowel which has been elongated by 6-1-102 then it is replaced by the letter ‘न्’।

Similarly, we can derive the form आदित्याः used in the verses.
अदितेरपत्यम् (पुमान्) = आदित्यः – a (male) descendant of Aditi
In the verses the विवक्षा is प्रथमा-बहुवचनम्, hence the form used is आदित्याः।

The derivation of the प्रातिपदिकम्‌ ‘आदित्य’ is similar to the derivation of the प्रातिपदिकम्‌ ’दैत्य’ as shown above. The प्रातिपदिकम् ‘आदित्य’ declines like राम-शब्दः।