In SN 35.85 (SA 232):
"It is, Ānanda, because it is empty of self and of what belongs to self that it is said, ‘Empty is the world."
"Yasmā ca kho, ānanda, suññaṃ attena vā attaniyena vā tasmā suñño lokoti vuccati."
"suññaṃ idaṃ attena vā attanīyena"
"this is empty of a Soul or aught pertaining to a Soul"
(Translation: O.H. de A. Wijesekera)
The Buddha said to Samṛddhi: “Eye is empty, empty of eternal and unchanging nature, empty of anything belonging
to self. Why is this so? This is nature as it is.
(SA 232) (Translation: Choong Mun-Keat)
Instrumental case forms "attena" and "attaniyena".
Attaniyena = Instrumental case of attaniya = belonging to atta，having an atta，of the nature of atta.
Attanīyena: pertaining to a Soul of a soul (what belongs to self), as in:
- iminā dutiyena in view of this (or by means of this)
- iddhipāṭihāriyena displays of supernormal powers
As meaning: "not constant/continual":
निज nija [ni-ja]
constant , continual (AV. Br. MBh.)
Instrumental > nijena
नि ni ind.
- in , into , within
ज ja [√ jan]
√ जन् jan
- to be born or produced , come into existence, to become , be (RV. - AV.)
- to generate , beget , produce , create , cause (RV. - AV.)
- to cause to be born (AV.)
As meaning: "one's own":
Niya，（adj．） [Sk．nija] = one’s own. => attaniya = one's own self.
निज nija [ni-ja]
in later Sanskṛit used as a reflex. possess. pron. = [ sva ] = my own , his own , our own.
Although निज nija means "one's own" in later Sanskrit *, "continual" or "one's own" are linked, in the sense that there is continuity of being.
Also, PTS & PED are giving "one's own", as the definition for niya.
Note that SA is the only version that addresses the "eternal and unchanging nature" of atta.
To conclude, the "constant (and continual)" of atta is to be preferred as a translation.
While "one's own" is not conflicting with the former - Being "continuous", Atta/atta is appropriated by one's own being.
“Bhikkhus, there being a self, would there be for me what belongs to a self?” [note: here, "what belongs to a self" is continuity.]
“Yes, venerable sir.”
“Or, there being what belongs to a self, would there be for me a self?”
“Yes, venerable sir.”
“Bhikkhus, since a self and what belongs to a self are not apprehended as true and established, then this standpoint for views, namely, ‘That which is the self is the world; after death I shall be permanent, everlasting, eternal, not subject to change; I shall endure as long as eternity’—would it not be an utterly and completely foolish teaching?”
"This self (atman) of mine that lies deep within my heart - it contains all actions, all desires, all smells, and all tastes; it has captured this whole world; it neither speaks nor pays any heed.
"It is Brahman. On departing from here after death, I will become that."
(Chāndogya Upaniṣad - ChUp. 3.14.4)
Let him meditate on the Self, which is made up of intelligence, and endowed with a body of spirit, with a form of light, and with an etherial nature, which changes its shape at will, is swift as thought, of true resolve, and true purpose, which consists of all sweet odours and tastes, which holds sway over all the regions and pervades this whole universe, which is speechless and indifferent;even as a grain of rice, or a grain of barley, or a grain of millet, or the smallest granule of millet, so is this golden Purusha in the heart; even as a smokeless light, it is greater than the sky, greater than the ether, greater than the earth, greater than all existing things;--that self of the spirit (breath) is my self: on passing away from hence I shall obtain that self. Verily, whosoever has this trust, for him there is no uncertainty. Thus spake Sāndilya, and so it is.
sa ātmānamupāsīta manomayam prāṇaśarīram bhārūpamākāśātmānaṃkāmarūpiṇam manojavasaṃ satyasaṃkalpaṃ satyadhṛtiṃ sarvagandhaṃ sarvarasaṃ sarvā anu diśaḥ prabhūtaṃ sarvamidamabhyāptamavākkamanādaraṃ yathā vrīhirvā yavo vā śyāmāko vā śyāmākataṇḍulo vaivamayamantarātmanpuruṣo hiraṇmayo yathā jyotiradhūmamevaṃ jyāyāndivo jyāyānākāśājjyāyānasyai pṛthivyai jyāyāntsarvebhyo bhūtebhyaḥ sa prāṇasyātmaiṣa ma ātmaitamita ātmānam pretyābhisambhaviṣyāmīti yasya syādaddhā na vicikitsāstīti ha smāha śāṇḍilya evametaditi.
(Śatapatha Brāhmaṇa - ŚBr. 10.6.3)
* (Later Sanskrit > Early post Vedic, etc.)