CC Ādi 2.67
ইন্দ্রারি–ব্যাকুলং লোকং মৃড়য়ন্তি যুগে যুগে ॥ ৬৭ ॥
kṛṣṇas tu bhagavān svayam
mṛḍayanti yuge yuge
ete — these; ca — and; aṁśa — plenary portions; kalāḥ — parts of plenary portions; puṁsaḥ — of the puruṣa-avatāras; kṛṣṇaḥ — Lord Kṛṣṇa; tu — but; bhagavān — the Supreme Personality of Godhead; svayam — Himself; indra-ari — the enemies of Lord Indra; vyākulam — full of; lokam — the world; mṛḍayanti — make happy; yuge yuge — at the right time in each age.
“All these incarnations of Godhead are either plenary portions or parts of the plenary portions of the puruṣa-avatāras. But Kṛṣṇa is the Supreme Personality of Godhead Himself. In every age He protects the world through His different features when the world is disturbed by the enemies of Indra.”
This statement of Śrīmad-Bhāgavatam (1.3.28) definitely negates the concept that Śrī Kṛṣṇa is an avatāra of Viṣṇu or Nārāyaṇa. Lord Śrī Kṛṣṇa is the original Personality of Godhead, the supreme cause of all causes. This verse clearly indicates that incarnations of the Personality of Godhead such as Śrī Rāma, Nṛsiṁha and Varāha all undoubtedly belong to the Viṣṇu group, but all of Them are either plenary portions or portions of plenary portions of the original Personality of Godhead, Lord Śrī Kṛṣṇa.