Today we will look at the form राजन्याः mNp from श्रीमद्भागवतम् verse 10.83.34.

तेऽन्वसज्जन्त राजन्या निषेद्धुं पथि केचन ।
संयत्ता उद्धृतेष्वासा ग्रामसिंहा यथा हरिम् ॥ १०-८३-३४ ॥

श्रीधर-स्वामि-टीका –
अन्वसज्जन्त पृष्ठतः सक्ता बभूवुः । निषेद्धुं प्रतिबन्धं कर्तुं केचन पुरतो गत्वा पथि संयत्ता बभूवुरित्यर्थः । उद्धृतेष्वासा ऊर्ध्वकृतचापाः । ग्रामसिंहाः श्वानो हरिं सिंहं यथेति ॥ ३४ ॥

Gita Press Translation – Lifting up their bows and prepared for a battle, some of those kings pursued my Lord with a view to obstructing Him on the way; but their attempt was no more successful than that of dogs to check the lion (34).

राज्ञोऽपत्यम् (पुमान्) जातिः = राजन्यः – the son of a kṣatriya king (from his kṣatriya wife)
In the verses the विवक्षा is प्रथमा-बहुवचनम्। Hence the form is राजन्याः।

(1) राजन् ङस् + यत् । By 4-1-137 राजश्वशुराद्यत्‌ – To denote the sense of अपत्यम् (descendent), the तद्धित: affix ‘यत्’ may be applied optionally following a syntactically related पदम् which ends in a sixth case affix and has either ‘राजन्’ or ‘श्वशुर’ as its base.
Note: The affix ‘यत्’ prescribed by this सूत्रम् is a अपवाद: (exception) to the default affix ‘अण्’ (prescribed by the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण्) in the case of ‘राजन्’ as well as the affix ‘इञ्’ (prescribed by the सूत्रम् 4-1-95 अत इञ्) in the case of ‘श्वशुर’।
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) राजन् ङस् + य । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।
Note: The letter ‘त्’ in the affix ’यत्’ is for the purpose of indicating the intonation (ref: 6-1-185 तित्स्वरितम्)।

Note: ‘राजन् 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) राजन् + 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 अङ्गम् ‘राजन्’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम्।

(4) राजन्य । By 6-4-168 ये चाभावकर्मणोः – When followed by a तद्धितः affix beginning with the letter ‘य्’, the term ‘अन्’ remains unchanged, provided the affix denotes neither the action (भावः) nor the object (कर्म)।
Note: In the absence of 6-4-168 the सूत्रम् 6-4-144 नस्तद्धिते would have applied to elide the ‘टि’-portion ‘अन्’ of the अङ्गम् ‘राजन्’।

The प्रातिपदिकम् ‘राजन्य’ declines like राम-शब्दः।

(5) राजन्य + जस् । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्‌।

(6) राजन्य + अस् । अनुबन्ध-लोपः by 1-3-7 चुटू and 1-3-9 तस्य लोपः। 1-3-4 न विभक्तौ तुस्माः prevents the ending letter ‘स्’ of ‘जस्’ from getting the इत्-सञ्ज्ञा ।

(7) राजन्यास् । 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.)

(8) राजन्याः । रुँत्व-विसर्गौ by 8-2-66 ससजुषो रुः and 8-3-15 खरवसानयोर्विसर्जनीयः।